text:
# How do I increase the sensitivity of Salmon Alevin?

I'm in a little bit of a bind with targeted single-cell sequencing. I'm trying to match up our reads to the targeted amplicon panel (418 targets), and all but one have matched successfully with Salmon Alevin. I have a transcript that produces many 75bp reads that only match the first 28bp of a target, and Alevin is ignoring those reads as a match (the 28bp sequence is genome-unique).

Here's an example read, with matched sequence:

qual FFFFFFFFFFFFFFFFFFFFFFFFFFFF,,,::,,:,:,,,,,,,,,,,,,,,,,:,,,,,,,,:,,,,,:,:
SNPs ...................................G.G.G..G.GC.....CG...CCGGGGGGGGG..GG..
ref GCTGCATAATCTCTTCATTCCGAGGAGCACCCCACCCCCACCCCCACCCCCACCCCATTCTTAAATTGTTTGG

As you may be able to see from the above sequence, the reads for this particular transcript get up to 28bp (sometimes with one or two errors), then the wheels start coming off the sequencer, showing an abundance of Gs. This was a NovaSeq run, and a polyG read is the same as no signal using its two-dye process, so I suspect that the sequencing stops after ~35bp, rather than actually synthesising Gs from thin air.

I have lots of these reads; there are about 400k reads that match the reference transcript (Cxcr4, just in case it matters), and about 250k of those reads have a G homopolymer that's at least 8bp in length.

Any ideas on what to do?

FWIW, the above match was taken from a Bowtie2 alignment I did on the reads. I could use Alevin for cell barcode correction only and do the UMI deduplication manually, but it seems a shame to do that when it's only one transcript (from 418) that's spoiling a fully-automated process.

I did try adding in an additional transcript that included the full sequence of a short-match read, but there seem to be too many errors in the non-matching sequence for any reads to count (at least... I assume that's why the counts are not coming through; I'm not quite sure how I can work out what's going on behind the scenes).

Is there any way to tweak Salmon Alevin to get it to accept these shorter matches? If I can change the kmer size, how do I do that?

End trimming is unlikely to help, because that's going to shorten the reads and make them less likely to map to the target sequence. I want a way to include these reads as valid hits to the target sequence.

• I cannot say that I follow why these particular reads are actually 28bp followed by gibberish but the default kmer size in salmon indexing is 31, hence reads shorter than inevitably go unmapped. You could index with a smaller k. Why exactly do these reads have these polyGs? Is that a consequence of how these targeted libraries are made, so is the fragment only 28bp of meaningful content? Jun 7 at 20:08
• Since the end is gobbledegook, you should quality trim. Jun 7 at 22:53

So, I think there are a few potential options here. Alevin is using selective-alignment internally to determine the mappings for the reads. So, even if you have a k-mer supporting the mapping, if you have gibberish for the rest of the read, the mapping score is going to be very poor and you're not going to recover that mapping locus. There are some parameters you can mess with to try to increase the sensitivity of mapping, though you should always be aware that upping the sensitivity a lot will mean there is less aggressive filtering early in the mapping process which can slow things down. The main parameter you should tweak to allow lower alignment scores is --minScoreFraction; the smaller this value the lower (worse) will be the permitted scores for valid mappings. Additionally, you can combine changes to the --minScoreFraction with the --softclip option to simply score the non-matching end of read as 0 (rather than a long deletion or large set of mismatches); this will lower the effect of bad read ends.

Another alternative you might consider is to try out alevin-fry for processing this data, and mapping the reads with the --sketch flag. This will only check certain structural constraints of the mapping and won't force a particular minimum alignment score. The caveat here is that dropping the requirement for alignment scoring can increase the rate of spurious mappings (reads deriving from elsewhere that spuriously map to some indexed target simply by virtue of sharing some sequence). In transcriptome wide analyses, this can be greatly mitigated by building an appropriate index and using a UMI resolution strategy that complements this expanded index. We've not examined this in detail for targeted single-cell sequencing. However, if you want to give it a try and run into any issues, feel free to drop an issue over on GitHub and we'd be happy to help work through it.

• Thank you; tweaking the minScoreFraction did the trick. I went from a max Cxcr4 read count per cell of 1 with default parameters, to 4 with minScoreFraction=0.5, to 26 with minScoreFraction=0.33.
– gringer
Jun 8 at 8:47
• Out of curiosity, did that require changing the kmer length during indexing? Jun 10 at 8:50

@ATPoint commented that the default kmer size in Salmon indexing is 31, which led me to a solution that involved altering the index generation step:

salmon index -t merged_salmon_$${targetName}.fasta -i salmonIndex_$${targetName}

I now have:

salmon index -t merged_salmon_$${targetName}.fasta -i salmonIndex_k11_$${targetName} -k 11

In other words, I changed the kmer size from its default of 31 to 11, which matches the BD-recommended seed substring length for the standard Bowtie2 approach ("-L 10", but I increased that to 11 because Salmon needs odd kmer sizes). I'm pretty sure that my 28bp-mapping reads won't be picked up with a kmer size of 31. Because this is targeted sequencing, I don't expect that a reduced kmer size will be an issue, but I'll keep a watch out for that.

I'm currently re-running the analysis. If it still doesn't work, then I'll see about adding in the tweaks suggested by @nomad.

Update: still not working, so I'll shift onto score tweaks.


text:
Ao Sun

MIT

## Time:

Friday, November 8, 2019 - 4:00pm to 5:00pm

## Location:

RH 306

One of the central topics in mean curvature flow is understanding the singularities. In 1995, Ilmanen conjectured that the first singularity appeared in a smooth mean curvature flow of surfaces must have multiplicity one. Following the theory of generic mean curvature flow developed by Colding-Minicozzi, we prove that a closed singularity with high multiplicity is not generic, in the sense that we may perturb the flow so that this singularity with high multiplicity can never show up. One of the main techniques is the local entropy, which is an extension of the entropy used by Colding-Minicozzi to study the generic mean curvature flow.

format: plain


text:
# Efficient out-of-place arbitrary rank GPU transpose

Summary: Is there an efficient out-of-place GPU tensor transpose operation that scales as $O(n)$ for tensors with $n$ total elements, regardless of the rank $d$? The naive algorithm costs $O(dn)$, since it requires $O(d)$ worth of index manipulation per entry.

Here is the current implementation of high rank tensor transpose in TensorFlow:

https://github.com/tensorflow/tensorflow/blob/master/tensorflow/core/kernels/transpose_functor_gpu.cu.cc#L27

It does a flat 1-D loop, deconstructs the index using $O(d)$ divisions by strides, and reconstructs the transposed index. Is there any index trickery / precomputation that would avoid the $O(d)$ cost per entry?

• I wonder if it's dominated by uncoalesced memory accesses or by the $O(d)$ index computation? I would've guessed uncoalesced loads are more expensive by far. It's worth checking that first I'd say. (e.g., devblogs.nvidia.com/parallelforall/…) – Kirill Nov 16 '16 at 16:41


text:
Change search

Search for new phenomena in events with three or more charged leptons in pp collisions at TeV with the ATLAS detector
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, High Energy Physics.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, High Energy Physics.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, High Energy Physics.
Number of Authors: 2878
2015 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 8, 138Article in journal (Refereed) Published
##### Abstract [en]

A generic search for anomalous production of events with at least three charged leptons is presented. The data sample consists of pp collisions at $$\sqrt{s}=8$$ TeV collected in 2012 by the ATLAS experiment at the CERN Large Hadron Collider, and corresponds to an integrated luminosity of 20.3 fb−1. Events are required to have at least three selected lepton candidates, at least two of which must be electrons or muons, while the third may be a hadronically decaying tau. Selected events are categorized based on their lepton flavour content and signal regions are constructed using several kinematic variables of interest. No significant deviations from Standard Model predictions are observed. Model-independent upper limits on contributions from beyond the Standard Model phenomena are provided for each signal region, along with prescription to re-interpret the limits for any model. Constraints are also placed on models predicting doubly charged Higgs bosons and excited leptons. For doubly charged Higgs bosons decaying to eτ or μτ, lower limits on the mass are set at 400 GeV at 95% confidence level. For excited leptons, constraints are provided as functions of both the mass of the excited state and the compositeness scale Λ, with the strongest mass constraints arising in regions where the mass equals Λ. In such scenarios, lower mass limits are set at 3.0 TeV for excited electrons and muons, 2.5 TeV for excited taus, and 1.6 TeV for every excited-neutrino flavour.

2015. no 8, 138
##### National Category
Physical Sciences
##### Identifiers
ISI: 000361002900001OAI: oai:DiVA.org:uu-264758DiVA: diva2:861447
##### Funder
Swedish Research Council
##### Note

ATLAS Collaboration, for complete list of authors see http://dx.doi.org/10.1007/JHEP08(2015)138

Available from: 2015-10-16 Created: 2015-10-16 Last updated: 2015-10-16Bibliographically approved

#### Open Access in DiVA

##### File information
File name FULLTEXT01.pdfFile size 1000 kBChecksum SHA-512
9e409f0ca0c5bbb413fc29945199cb07faaa023213fea3a08e705fa8fbb2e6d6c369ce3400ffdef4c002e2476c238244ae05a12d497eed688f47ed53c1b2f3cf
Type fulltextMimetype application/pdf

Publisher's full text

#### Search in DiVA

##### By author/editor
Bergeås, Elin KuutmannBrenner, RichardBuszello, Claus P.Ekelöf, TordEllert, MattiasFerrari, ArnaudIsaksson, CharlieMadsen, AlexanderÖhman, HenrikPelikan, DanielRangel-Smith, Camilla
##### By organisation
High Energy Physics
##### In the same journal
Journal of High Energy Physics (JHEP)
##### On the subject
Physical Sciences


text:
Authors: Clark R. Dohrmann and Olof B. Widlund

Title: An Alternative Coarse Space for Irregular Subdomains and an Overlapping Schwarz Algorithm

Abstract

In earlier work on domain decomposition methods for elliptic problems in the plane,
an assumption that each subdomain is triangular, or a union of
a few coarse triangles, has often been made. This is
similar to what is required in geometric multigrid theory
and is unrealistic if the subdomains are produced by a mesh partitioner.
In an earlier paper, coauthored with Axel Klawonn, the authors introduced
a coarse subspace for an overlapping Schwarz method
with one degree of freedom for each subdomain
vertex and one for each subdomain edge. A condition number
bound proportional to $(1+\log(H/h))^2(1+H/\delta)$
was established assuming only that the subdomains are
John domains; here $H/\delta$ measures the relative overlap between
neighboring subdomains and $H/h$ the maximum
number of elements across individual subdomains. We were
also able to relate the rate of convergence to a parameter
in an isoperimetric inequality for the subdomains into which
the domain of the problem has been partitioned.

In this paper, the dimension of the coarse subspace is decreased
by using only one degree of freedom for each subdomain
vertex; if all subdomains have three edges, this leads to a reduction
of the dimension of the coarse subspace by approximately a factor four.
In addition, the condition number bound is shown to be proportional to
$(1+\log(H/h))(1+H/\delta)$ under a quite mild assumption on the
relative length of adjacent subdomain edges.

In this study, the subdomains are assumed to be uniform in
the sense of Peter Jones. As in our earlier work, the results are insensitive
to arbitrary large jumps in the coefficients of the elliptic problem across
the interface between the subdomains.

Numerical results are presented which confirm the
theory and demonstrate the usefulness of the algorithm for a variety
of mesh decompositions and distributions of material properties. It is
also shown that the new algorithm often converges faster than the older
one in spite of the fact that the dimension of the coarse space has been
decreased considerably.


text:
INVESTIGATION OF TIRE FORCE TRANSMISSION ON INTERACTION WITH SLUSH

## Publications

/ Export Citation / / / Text size:

#### Transport Problems

Silesian University of Technology

Subject: Economics, Transportation, Transportation Science & Technology

eISSN: 2300-861X

15
21
Visit(s)
0
Comment(s)
0
Share(s)

SEARCH WITHIN CONTENT

FIND ARTICLE

Volume / Issue / page

Archive
Volume 16 (2021)
Volume 15 (2020)
Volume 14 (2019)
Volume 13 (2018)
Volume 12 (2017)
Volume 11 (2016)
Volume 10 (2015)
Related articles

VOLUME 14 , ISSUE 1 (Apr 2019) > List of articles

### INVESTIGATION OF TIRE FORCE TRANSMISSION ON INTERACTION WITH SLUSH

Keywords : tire, slush layer, sub-block, friction force

Citation Information : Transport Problems. Volume 14, Issue 1, Pages 13-21, DOI: https://doi.org/10.21307/tp.2019.14.1.2

Published Online: 23-April-2019

### ARTICLE

#### ABSTRACT

The main parameters describing the interaction between a tire and the road are forces transmitted by a tire. This paper presents experimental and theoretical research of mechanism of force transmission between a tire and slush-covered pavement. The experimental research was conducted in the internal drum test facility at the Karlsruhe Institute of Technology in Germany. The theoretical research presents a mathematical model of the system “sub-block–slush layer–drum” focusing on slush behavior. The model evaluates mass change velocity of slush layer, mass, and physical–mechanical properties of sub-block. Slush was analyzed as a multi-layer bulk. The obtained velocities of slush layers and friction forces from the model allowed us to determine the generated heat per time unit at each layer. It was found that the top layer of slush has the highest velocity and heat flow values compared to other layers.

## 1. INTRODUCTION

In regions with extreme winters such as Scandinavian and Baltic regions, road safety during winter season is a matter of utmost concern for transportation officials. Driving conditions in winter can deteriorate and vary dramatically because of snowfall and ice formation, causing a significant reduction in tire friction and increasing the risk of accidents [1-4].

In order to ensure traffic safety, the controllability of a vehicle in all seasons and weather conditions is of special importance. When tires come in a direct contact with the pavement, a grip is formed, which directly controls a vehicle; parameters of tires have a great influence on the control, stability, and safety of the vehicle [5].

To engineer tires in a better way to be used efficiently in winters, the factors influencing the friction and the contact mechanics should be well studied. Besides the behavior of rubber material, the friction mechanisms of rubber are very complex as well. The viscoelastic material properties of rubber cause a complicate friction behavior, which depends on the contact area, the sliding velocity, the normal pressure, and the ambient temperature. The rubber friction, in general, is dominated by four single mechanisms [6, 7]:

• Hysteresis – caused by internal damping of the rubber material.

• Adhesion – described as an increase in physical bonding between two bodies, when they are brought in a close contact.

• Viscous friction – occurs in lubricated contacts.

• Cohesion – the generation of wear particles or cracks on the rubber surface.

The total friction force is assumed to be the sum of these components.

Experimental tire testing can be classified into laboratory and road measurements. Testing tires outdoor on winter tracks such as snow, ice or slush is very challenging, as track and ambient parameters continuously change. Indoor testing allows us to control these parameters; hence, measurements become much more reproducible than outdoor measurements. As a tire is a very complexly engineered object, to reduce the difficulty and complexity of the tire testing, it can be practicable to test only parts of a tire. For example, the study of the interaction between tire tread and road surface can be done with a single tread block. It allows investigating the dominating friction mechanisms [8].

There are studies on the mechanism of force transmission of tire in snow or ice [9-12] and the friction mechanism between tire tread blocks and ice or snow-covered pavement [13-15], but there is a lack of studies analyzing the interaction between a tire and slush. The closest investigation is presented by Lee and Huang [16]. The authors have used the wet snow definition described by the International Snow Classification [17] and presented the outdoor measurements using a special test vehicle. Meanwhile, this paper studies the interaction between a tire and slush, which, according to the International Snow Classification, is described as soaked snow with water and its volume fraction is higher than 15%.

## 2. EXPERIMENTAL AND THEORETICAL INVESTIGATION

### 2.1. Methodology of experimental research

The measurement of tire force transmission was conducted using the internal drum test bench at the Karlsruhe Institute of Technology in Germany. The test facility provided the opportunity to perform measurements on different track surfaces and under various operating conditions. It consisted of the drum with a diameter of 3.8 m, wherein a tire, mounted on a facility wheel suspension, rolled on the installed track (Fig. 1). Wheel and drum could be tested independently for braking and traction evaluation. Sideslip and camber angles and vertical load were adjusted by the hydraulic system. The test facility was surrounded by a climate-controlling chamber with an air-conditioning system that cooled down the testing room to –20 °C.

##### Fig. 1.

Measurements of tire parameters: a) internal drum test facility and b) tire rolling on slush-covered drum

Tire–slush measurements were performed with the initial height of slush layer being 4 cm. It was obtained by mixing 110 l water with 22 l of fresh snow. The mixture was rotated in the rotating drum at about 55 km/h to spread it equally on the drum surface. Then, one tire acceleration measurement was conducted, which took about 14 s. The main parameters of interaction were measured: wheel load (Fz), longitudinal friction force (Fx ), tire angular velocity (ωT), drum angular velocity (ωdr), dynamic radius of the wheel (Rdyn), and slip (Sx). A special 205/55 R16 winter tire was used, and its tread pattern is shown in Fig. 2a. The tread height was 8 mm.

##### Fig. 2.

Concept of tire–slush interaction: a) tire tread parts and b) sub-block interaction with a slush layer

### 2.2. Theoretical analysis of tire–slush interaction

The tire–slush interaction measurements were conducted at the macro-level and main parameters (Fz, Fx, Sx, etc.) were obtained. For the evaluation of contact parameters between tire and slush, it was assumed to conduct measurements at the micro-level, focusing on the mathematical evaluation of slush and its behavior. For this reason, an interaction between sub-block and slush layer (Fig. 2b) was analyzed. The sub-block is a part of tread block separated with sipes (Fig. 2b). A tread block usually has four or five sub-blocks that are in direct contact with the road surface.

To evaluate the friction between the sub-block and top layer of slush, the velocities of sub-block and top slush layer should be known. When slush is moved in a drum, both bottom and top slush layers move and their velocities are different. The movement of the slush layers depends on its dynamic viscosity. Slush dynamic viscosity depends on multi-component bulk (snow crystals, water, and air). Slush, as the multi-component bulk, is compressible; therefore, its dynamic viscosity depends on bulk compressibility.

In the presented theoretical model (Fig. 3), the mass change velocity is evaluated.

##### Fig. 3.

Dynamic model of system: sub-block–slush layers–drum

The interaction between sub-block and slush layer also depends on the physical–mechanical properties of sub-block material and geometric parameters (height, width, and length). The physical– mechanical properties were evaluated through stiffness (Ke) and damping (Ce) coefficients. The mass of sub-block was also evaluated in the model.

Dynamic viscosity of slush is calculated as follows:

##### (1)

where is μSl,0 the initial dynamic viscosity, and aSl and bSl are the coefficients.

Inertial number ISl is defined by [18]

##### (2)

where p0 is pressure (p0 = 105 Pa), v is the velocity of slush, h is the slush height, and mSl is the mass of slush, calculated as follows:

##### (3)

where ρSl is the density of slush and VSl is the volume of slush.

The equation of motion for first (bottom) slush layer can be expressed as follows:

##### (4)

where mSl,1 is the mass of slush and CSl,1 is the damping coefficient. The velocity of slush mass of first Sl,1 layer is calculated as follows:

##### (5)
$m˙Sl,1=dmsl,1dt=ρ˙Sl,1VSl,1+ρSl,1V˙Sl,1.$

The friction force between the first layer of slush and drum can be expressed as follows:

##### (6)

where µSl,1 is the dynamic viscosity of first slush layer.

The equation of motion for i-th slush layer is equal

##### (7)
$mSl,i(t)q¨Sl,i=−Ff,Sl,i−1,i(q˙Sl,i−1,q˙Sl,i)sign(q˙Sl,i,q˙Sl,i−1)−Ff,Sl,i,i+1(q˙Sl,i,q˙Sl,i+1)sign(q˙Sl,i,−q˙Sl,i+1)−cSl,iq˙Sl,i−m˙Sl,i,q˙Sl,i,i=2,…,N−1.$

Then, the equation of motion for last (top) slush layer is equal:

##### (8)
$mSl,Nq¨Sl,N=−cSl,Nq˙Sl,N−Ff,Sl,N−1,N(q˙Sl,N−1,q˙Sl,N)sign(q˙Sl,N−q˙Sl,N−1)−Ff,Sl,T(q˙Sl,N,q˙N+1)sign(q˙Sl,N−q˙N+1).$

The equation of motion of sub-block is equal:

##### (9)

where msub–block is the mass of sub-block, ke and ce are the stiffness and damping coefficients, respectively, and γ is the angle between radius and centrifugal force direction, calculated as follows:

##### (10)
$tg(γ)=qN+1−VTtRdyn.$

The friction force between slush and tire was evaluated using the friction model presented in [19]. Then, friction force can be expressed as

##### (11)

where $△vSl=q˙N+1−q˙Sl,N$ is the difference between the slush velocities, μv0, μv1, μp0, μp1 are force coefficients, and Fz(t) is the normal force of wheel load.

The obtained velocities of slush layers and friction forces allow us to determine the generated heat per time unit at each layer. This can provide additional information about how slush layers interact with each other.

## 3. RESULTS AND DISCUSSION

The tire–slush interaction measurement was conducted at about 48 km/h of drum speed. The tire pressure was 2.2 bar, with the camber angle of 0°. The wheel load was about 4000 N. The ambient temperature of surrounding area varied from 0 °C to 1 °C. The force coefficient as the ratio of longitudinal friction force (Fx) and normal force (Fz) was expressed and its variation during the measurement is presented in Fig. 4. The maximum value reached 0.3.

##### Fig. 4.

Variation of longitudinal force coefficient

The sub-block load was expressed from measured normal force (Fz) and tire print was obtained at about 4200 N wheel load and 2.2 bar tire pressure. The normal force that pushes the tire tread block into the top layer of slush was determined. Its variation during the measurement is shown in Fig. 5.

##### Fig. 5.

To solve the motion equations derived in the second chapter, Δt = 10−5 integration time was taken. The height of slush layer was divided into 9 elements, which varied from 40 mm (initial height) to 20 mm. The material of sub-block was assumed as a rubber, and density was taken equal to 1100 kg/m3. The stiffness coefficient of rubber was taken ke = 19 kN/m and damping coefficient equal to ce = 2.0 Ns/m. The mass of sub-block was 0.88 g. The variation between 8th and 9th (top) layers velocities over time is shown in Fig. 6.

##### Fig. 6.

Velocities of slush layers

Fig. 6 shows that the evaluated velocity of top slush layer, which is in direct contact with the tire, is higher than the layer below. This shows that the top layer of slush has highest influence on the friction mechanism between tire and slush. The velocity variation of sub-block over time is presented in Fig. 7.

##### Fig. 7.

Velocity of sub-block

The sub-block velocity fluctuation shown in Fig. 7 is similar to the velocity of top slush layer presented in Fig. 6. There is a slight difference between the values of velocities. It shows that there is a friction between the sub-block and the top layer of slush.

The developed mathematical model enables us to evaluate the heat flow at each slush layer. The variation between the heat flow at 8th and 4th layers over time is presented in Figs. 8 and 9, respectively.

##### Fig. 8.

Heat flow at the 8th slush layer

##### Fig. 9.

Heat flow at the 4th slush layer

The performed heat generation analysis showed that highest heat value is generated at the top layer of slush, which is in direct contact with a tire. However, lower layers generate low heat values compared to the top layers. The value of generated heat decreases going from the top layers to the bottom.

## 4. CONCLUSIONS

This study has presented experimental and theoretical research of interaction between a tire and slush. The experimental study allowed us to determine the main parameters of tire–slush interaction as longitudinal friction force (Fx), normal force (Fz), tire angular velocity (ωT), tire dynamic radius (Rdyn ), and slip (Sx). In the theoretical research, a mathematical model was created. The tire was analyzed at the micro-level and only one part of tire tread block – a sub-block – was analyzed focusing on slush behavior. Slush was analyzed as a multi-layer bulk and mass change velocity. The physical– mechanical properties of sub-block material and its mass were evaluated. The obtained velocities and friction forces of slush layers allowed us to calculate the heat generation at each slush layer. The results showed that the highest velocity and maximum heat generation were observed at the top layer of slush, which is in the direct contact with the tire.

## Acknowledgment

This work has been supported by the Research Council of Lithuania Fund within the project “Investigation of tribological micro-macro processes in multi-phase layer with ice-snow particles and their contribution to tire-layer-surface system”, project code P-MIP-17-233.

## References

1. Usman, T. & Fu, L. & Moreno-Miranda, F.L. Quantifying safety benefit of winter road maintenance activities at an operational level. Accident Analysis and Prevention. 2010. Vol. 42. P. 1878-1887.
[CROSSREF]
2. Usman, T. & Fu, L. & Moreno-Miranda, F.L. A dissagregate model for quantifying the safety effects of winter road maintenance activities at an operational level. Accident Analysis and Prevention. 2012. Vol. 48. P. 368-378.
[CROSSREF]
3. Hayat, B.R. & Debbarh, M. & Antoniou, C. & Yannis, G. & et al. Explaining the road accident risk: weather effects. Accident Analysis and Prevention. 2013. Vol. 60. P. 456-465.
[CROSSREF]
4. Seeherman, J. & Liu, Y. Effects of extraordinary snowfall on traffic safety. Accident Analysis and Prevention. 2015. Vol. 81. P. 194-203.
[CROSSREF]
5. Sapragonas, J. & Keršys, A. & Makaras, R. & et al. Research of the influence of tire hydroplaning on directional stability of vehicle. Transport. 2014. Vol. 28. No. 8. P. 374-380.
[CROSSREF]
6. Ripka, S. Experimental investigation and modeling of tire tread block friction on ice. PhD thesis. Leibniz Universitat Hannover. 2012. 111 p.
7. Ignatyev, A.P. & Ripka, S. & Mueller, N. & et al. Tire ABS-braking prediction with lab tests and friction simulations. Tire Science and Technology. 2015. Vol. 43. No. 4. P. 260-275.
[CROSSREF]
8. Ripka, S. & Lind, H. & Wangenheim, M. & et al. Investigation of friction mechanisms of siped tire tread blocks on snowy and icy surfaces. Tire Science and Technology. 2012. Vol. 10. No. 1. P. 1-24.
[CROSSREF]
9. Giessler, M. & Gauterin, F. & Wiese, K. & et al. Influence of friction heat on tire traction on andand snow. Tire Science and Technology. 2010. Vol. 38. No. 1. P. 4-23.
[CROSSREF]
10. Lee, H.J. & Huang, D. & Johnson, H.T. & et al. Slip-based experimental studies of a vehicle interacting with natural snowy terrain. Journal of Terramechanics. 2012. Vol. 49. P. 233-244.
[CROSSREF]
11. Bhoopalam, K.A. & Sandu, C. & Taheri, S. Experimental investigation of pneumatic tire performance on ice: Part 1 – Indoor study. Journal of Terramechanics. 2015. Vol. 60. P. 43-54.
[CROSSREF]
12. Bhoopalam, K.A. & Sandu, C. & Taheri, S. Experimental investigation of pneumatic tire performance on ice: Part 2 – Outdoor study. Journal of Terramechanics. 2015. Vol. 60. P. 55-62.
[CROSSREF]
13. Skouvaklis, G. & Blackford, R.J. & Koutsos, V. Friction of rubber on ice: A new machine, influence of rubber properties and sliding parameters. Tribology International. 2012. Vol. 49. P. 44-52.
[CROSSREF]
14. Ella, S. & Formagne, Y.P. & Koutsos, V. & et al. Investigation of rubber friction on snow for tyres. Tribology International. 2013. Vol. 59. P. 292-301.
[CROSSREF]
15. Klapproth, C. & Kessel, M. T. & Wiese, K. & et al. And advanced viscous model for rubber-ice friction. Tribology International. 2016. Vol. 99. P. 169-181.
[CROSSREF]
16. Lee, H.J. & Huang, D. Vehicle wet snow interaction: testing, modeling and validation. Journal of Terramechanics. 2016. Vol. 67. P. 233-244.
[CROSSREF]
17. Fiertz, C. & Armstrong, R.L. & Durand, Y. & Etchevers, P. & Greene, E. & McClung, D.M. & Nishimura, K. & Sayawali, P.K. & Sokratov, S. A. The International Classification for Seasonal Snow on the Ground. Technical Documents in Hydrology No. 83. IACS Contribution No. 1. UNESCO: Paris. 2009. 80 p.
18. Cruz, F. & Emam, S. & Prochnow, M. & et al. Rheophysics of dense granular materials: Discrete simulation of plane shear flows. Physical Review E. 2005. Vol. 72. P. 1-24.
[CROSSREF]
19. Moldenhauer, P. Modellierung un Simulation der Dynamik und des Kontakts von Reifenpofilblöcken. PhD thesis. Technische Universität Bergakademie Freiberg. 2010. 152 p. [In Germany: Modelhaurer, P. Modeling and simulation of the dynamics and the contact of tire tread blocks. PhD thesis. Freiberg Technical University].

### FIGURES & TABLES

Fig. 1.

Measurements of tire parameters: a) internal drum test facility and b) tire rolling on slush-covered drum

Fig. 2.

Concept of tire–slush interaction: a) tire tread parts and b) sub-block interaction with a slush layer

Fig. 3.

Dynamic model of system: sub-block–slush layers–drum

Fig. 4.

Variation of longitudinal force coefficient

Fig. 5.

Fig. 6.

Velocities of slush layers

Fig. 7.

Velocity of sub-block

Fig. 8.

Heat flow at the 8th slush layer

Fig. 9.

Heat flow at the 4th slush layer

### REFERENCES

1. Usman, T. & Fu, L. & Moreno-Miranda, F.L. Quantifying safety benefit of winter road maintenance activities at an operational level. Accident Analysis and Prevention. 2010. Vol. 42. P. 1878-1887.
[CROSSREF]
2. Usman, T. & Fu, L. & Moreno-Miranda, F.L. A dissagregate model for quantifying the safety effects of winter road maintenance activities at an operational level. Accident Analysis and Prevention. 2012. Vol. 48. P. 368-378.
[CROSSREF]
3. Hayat, B.R. & Debbarh, M. & Antoniou, C. & Yannis, G. & et al. Explaining the road accident risk: weather effects. Accident Analysis and Prevention. 2013. Vol. 60. P. 456-465.
[CROSSREF]
4. Seeherman, J. & Liu, Y. Effects of extraordinary snowfall on traffic safety. Accident Analysis and Prevention. 2015. Vol. 81. P. 194-203.
[CROSSREF]
5. Sapragonas, J. & Keršys, A. & Makaras, R. & et al. Research of the influence of tire hydroplaning on directional stability of vehicle. Transport. 2014. Vol. 28. No. 8. P. 374-380.
[CROSSREF]
6. Ripka, S. Experimental investigation and modeling of tire tread block friction on ice. PhD thesis. Leibniz Universitat Hannover. 2012. 111 p.
7. Ignatyev, A.P. & Ripka, S. & Mueller, N. & et al. Tire ABS-braking prediction with lab tests and friction simulations. Tire Science and Technology. 2015. Vol. 43. No. 4. P. 260-275.
[CROSSREF]
8. Ripka, S. & Lind, H. & Wangenheim, M. & et al. Investigation of friction mechanisms of siped tire tread blocks on snowy and icy surfaces. Tire Science and Technology. 2012. Vol. 10. No. 1. P. 1-24.
[CROSSREF]
9. Giessler, M. & Gauterin, F. & Wiese, K. & et al. Influence of friction heat on tire traction on andand snow. Tire Science and Technology. 2010. Vol. 38. No. 1. P. 4-23.
[CROSSREF]
10. Lee, H.J. & Huang, D. & Johnson, H.T. & et al. Slip-based experimental studies of a vehicle interacting with natural snowy terrain. Journal of Terramechanics. 2012. Vol. 49. P. 233-244.
[CROSSREF]
11. Bhoopalam, K.A. & Sandu, C. & Taheri, S. Experimental investigation of pneumatic tire performance on ice: Part 1 – Indoor study. Journal of Terramechanics. 2015. Vol. 60. P. 43-54.
[CROSSREF]
12. Bhoopalam, K.A. & Sandu, C. & Taheri, S. Experimental investigation of pneumatic tire performance on ice: Part 2 – Outdoor study. Journal of Terramechanics. 2015. Vol. 60. P. 55-62.
[CROSSREF]
13. Skouvaklis, G. & Blackford, R.J. & Koutsos, V. Friction of rubber on ice: A new machine, influence of rubber properties and sliding parameters. Tribology International. 2012. Vol. 49. P. 44-52.
[CROSSREF]
14. Ella, S. & Formagne, Y.P. & Koutsos, V. & et al. Investigation of rubber friction on snow for tyres. Tribology International. 2013. Vol. 59. P. 292-301.
[CROSSREF]
15. Klapproth, C. & Kessel, M. T. & Wiese, K. & et al. And advanced viscous model for rubber-ice friction. Tribology International. 2016. Vol. 99. P. 169-181.
[CROSSREF]
16. Lee, H.J. & Huang, D. Vehicle wet snow interaction: testing, modeling and validation. Journal of Terramechanics. 2016. Vol. 67. P. 233-244.
[CROSSREF]
17. Fiertz, C. & Armstrong, R.L. & Durand, Y. & Etchevers, P. & Greene, E. & McClung, D.M. & Nishimura, K. & Sayawali, P.K. & Sokratov, S. A. The International Classification for Seasonal Snow on the Ground. Technical Documents in Hydrology No. 83. IACS Contribution No. 1. UNESCO: Paris. 2009. 80 p.
18. Cruz, F. & Emam, S. & Prochnow, M. & et al. Rheophysics of dense granular materials: Discrete simulation of plane shear flows. Physical Review E. 2005. Vol. 72. P. 1-24.
[CROSSREF]
19. Moldenhauer, P. Modellierung un Simulation der Dynamik und des Kontakts von Reifenpofilblöcken. PhD thesis. Technische Universität Bergakademie Freiberg. 2010. 152 p. [In Germany: Modelhaurer, P. Modeling and simulation of the dynamics and the contact of tire tread blocks. PhD thesis. Freiberg Technical University].


text:
### Author Topic: Textbook error?  (Read 401 times)

#### Min Gyu Woo

• Full Member
• Posts: 29
• Karma: 12
##### Textbook error?
« on: September 14, 2018, 02:41:21 PM »
At the bottom of the page 19, it states that

Re$[(\overline{z - i\alpha})(z-s)]=0$

to show that the two segments are perpendicular.

However, on the next page it continues the proof by writing

$2$Re$[(\overline{z - i\alpha})(z-s)]=0$

Where did the $2$ come from?

#### Zhiyuan Cheng

• Newbie
• Posts: 1
• Karma: 0
##### Re: Textbook error?
« Reply #1 on: September 16, 2018, 01:31:24 PM »
They multiplied both sides by 2 so that there won't be tons of 1/2 in the calculation.


text:
# using \pgfkeys to set style parameters being passed to tkz-euclide

I've been using pstricks for a long time and feel very much at home there. But, recently I decided I want to learn tikz since that seems to integrate better with beamer. However, I keep running into road blocks. While the manual can be useful, it also gives me headaches for things that would be straight-forward in pstricks but have a completely different (and for me, non-intuitive) approach in tikz.

For example, I want to use pgfkeys to set the style parameters for points: their color, their fill-color, their size. But my invocation of \pgfkeys seem to get ignored. I've tried various approaches. Some lead to errors and other to no effect. Here's what my first attempt at this looked like for which the desired result did not take effect.

\documentclass{article}
\usepackage[dvipsnames]{xcolor}
\usepackage{tkz-euclide}
\pagestyle{empty}
\begin{document}

I would like something that looks like:\vspace{1cm}\par
\begin{tikzpicture}[scale=0.25]
\tkzDefPoint(0,0){A}
\tkzDefShiftPoint[A](70:8){B}
\tkzDefShiftPoint[A](30:5){C}
\tkzDefShiftPoint[A](-30:10){D}
\tkzDefShiftPoint[A](-130:7){E}

%% first scope
\begin{scope}[line width=4]
\tkzDrawPoints[color=blue,fill=red](A,B,C)
\end{scope}

%% second scope
\begin{scope}[line width=2]
\tkzDrawPoints[color=red,fill=yellow](D,E)
\end{scope}
\end{tikzpicture}

Here the code is set up more along the lines of how I would like to write
it, but the results are not what I expected.\vspace{1cm}\par
\begin{tikzpicture}[scale=0.25]
\tkzDefPoint(0,0){A}
\tkzDefShiftPoint[A](70:8){B}
\tkzDefShiftPoint[A](30:5){C}
\tkzDefShiftPoint[A](-30:10){D}
\tkzDefShiftPoint[A](-130:7){E}

%% first scope
\begin{scope}[line width=4]
\pgfkeys{/drawpoint/.style={color=blue,fill=red}}
\tkzDrawPoints(A,B,C)
\end{scope}

%% second scope
\begin{scope}[line width=2]
\tkzDrawPoints[color=red,fill=yellow](D,E)
\end{scope}
\end{tikzpicture}

\end{document}

which produces

I've tried to find an answer in the pgfkeys question posted here. But, I'm getting very lost and very confused.

-

Alain Matthes is the author of the tkz-collection. He might not yet be around so I will give an answer a try.

Looking at the file tkz-obj-points.tex of version 1.16c, we can see the definition for \tkzDrawPoints as

\def\tkzDrawPoints{\pgfutil@ifnextchar[{\tkz@drawpts}{\tkz@drawpts[]}}
%<--------------------------------------------------------------------------–>
\def\tkz@drawpts[#1](#2){%
\begingroup
\pgfkeys{/drawpoint/.cd}
\pgfqkeys{/drawpoint}{#1}
\foreach \point in {#2}{%
\node[point style] at (\point) {};}
\endgroup
}

We also see

\pgfkeys{/drawpoint/.cd,
size/.code    = {\tikzset{point style/.append style={%
minimum size = #1*\pgflinewidth}}},
color/.code    = {\tikzset{point style/.append style={%
draw = #1}}},
shape/.code    = {\tikzset{point style/.append style={%
shape=#1}}},
fill/.code    = {\tikzset{point style/.append style={%
fill=#1}}}                                     }

So your call to \pgfkeys{/drawpoint... gets over-written every time you use \tkzDrawPoints as this command internally uses the same \pgfkeys drawpoint key. You should use \tikzset instead to style your points like:

%% first scope
\begin{scope}[line width=4]
\tikzset{point style/.style={fill=red,draw=blue,minimum size=0.9cm,shape=circle}}
\tkzDrawPoints(A,B,C)
\end{scope}

or you can stick with the definition of \tkzDrawPoints:

    %% first scope
\begin{scope}[line width=4]
%       \tikzset{point style/.style={fill=red,color=blue,minimum size=0.9cm,shape=circle}}
\tkzDrawPoints[fill=red,color=blue,shape=circle](A,B,C)
\end{scope}

Note also that you can use size as an option to \tkzDrawPoints. I have to admit that I get unpredictable results with combinations of line width option as you used them in this use-case and size.

## Edit 1

You can see the following definition of the key point style in tkz-base.cfg.

\tikzset{point style/.style={draw         = \tkz@euc@pointcolor,
inner sep    = 0pt,
shape        = \tkz@euc@pointshape,
minimum size = \tkz@euc@pointsize*\pgflinewidth,
fill         = \tkz@euc@pointcolor!50}}

You can set the options to your liking. An example is given in the tkz-base manual. Note that the tkz-collection is not an official part of tikz. Rather, it is a collection of tikz-based packages. Here is an example from page 42 of the manual:

\begin{tikzpicture}
\tikzset{point style/.style={%
draw = blue,
inner sep = 0pt,
shape = circle,
minimum size = 6pt,
fill = red!20}}
\tkzDefPoint(1,3){A}
\tkzDefPoint(4,1){B}
\tkzDefPoint(0,0){O}
\tkzDrawPoint(A)
\tkzDrawPoint(B)
\tkzDrawPoint(O)
\end{tikzpicture}

And here it is for your use-case.

%% first scope
\begin{scope}[line width=4]
\tikzset{point style/.style={%
draw = blue,
inner sep = 0pt,
shape = circle,
minimum size = 24pt,
fill = red!20}}
\tkzDrawPoints[fill=red,color=blue,shape=circle](A,B,C)
\end{scope}

Using the definition of \tkzDrawPoint, you can also specify other shapes. Here is an example from page 43

\begin{tikzpicture}[scale=.5]
\tkzDefPoint(1,3){A}
\tkzDefPoint(4,1){B}
\tkzDefPoint(0,0){O}
\tkzDrawPoint[shape=cross out,size=12,color=red](A)
\tkzDrawPoint[shape=cross,size=12,color=blue](B)
\tkzDrawPoint[size=12,color=green](O)
\tkzDrawPoint[size=12,color=blue,fill=yellow]({2,2})
\end{tikzpicture}

Of course, you can also set the point style options to affect all points.

-
Where do I read more to better understand this syntax? There's nothing in the pgf manual about \tikzset{point style/.style=....} otherwise I might have tried it. I had looked at the source code you mention, but again (probably because I'm unfamiliar with the syntax) I didn't realize that the keys were overwriting each other because I thought I was making a different call to them using .style instead of .cd. – A.Ellett Dec 27 '12 at 22:23


text:
CryptoDB

Luowen Qian

Publications

Year
Venue
Title
2022
CRYPTO
Pseudorandom states, introduced by Ji, Liu and Song (Crypto'18), are efficiently-computable quantum states that are computationally indistinguishable from Haar-random states. One-way functions imply the existence of pseudorandom states, but Kretschmer (TQC'20) recently constructed an oracle relative to which there are no one-way functions but pseudorandom states still exist. Motivated by this, we study the intriguing possibility of basing interesting cryptographic tasks on pseudorandom states. We construct, assuming the existence of pseudorandom state generators that map a $\lambda$-bit seed to a $\omega(\log\lambda)$-qubit state, (a) statistically binding and computationally hiding commitments and (b) pseudo one-time encryption schemes. A consequence of (a) is that pseudorandom states are sufficient to construct maliciously secure multiparty computation protocols in the dishonest majority setting. Our constructions are derived via a new notion called pseudorandom function-like states (PRFS), a generalization of pseudorandom states that parallels the classical notion of pseudorandom functions. Beyond the above two applications, we believe our notion can effectively replace pseudorandom functions in many other cryptographic applications.
2019
TCC
We construct the first adaptively secure garbling scheme based on standard public-key assumptions for garbling a circuit $C: \{0, 1\}^n \mapsto \{0, 1\}^m$ that simultaneously achieves a near-optimal online complexity $n + m + \textsf {poly} (\lambda , \log |C|)$ (where $\lambda$ is the security parameter) and preserves the parallel efficiency for evaluating the garbled circuit; namely, if the depth of C is d, then the garbled circuit can be evaluated in parallel time $d \cdot \textsf {poly} (\log |C|, \lambda )$ . In particular, our construction improves over the recent seminal work of [GS18], which constructs the first adaptively secure garbling scheme with a near-optimal online complexity under the same assumptions, but the garbled circuit can only be evaluated gate by gate in a sequential manner. Our construction combines their novel idea of linearization with several new ideas to achieve parallel efficiency without compromising online complexity.We take one step further to construct the first adaptively secure garbling scheme for parallel RAM (PRAM) programs under standard assumptions that preserves the parallel efficiency. Previous such constructions we are aware of is from strong assumptions like indistinguishability obfuscation. Our construction is based on the work of [GOS18] for adaptively secure garbled RAM, but again introduces several new ideas to handle parallel RAM computation, which may be of independent interests. As an application, this yields the first constant round secure computation protocol for persistent PRAM programs in the malicious settings from standard assumptions.

Coauthors

Prabhanjan Ananth (1)
Kai-Min Chung (1)
Henry Yuen (1)


text:
# Experimental Theoretical Physics

I was talking with some other physicists about my “Black Box Theory” thought experiment, where theorists have to compete with an impenetrable block of computer code. Even if the theorists come up with a “better” theory, that theory won’t predict anything that the code couldn’t already. If “predicting something new” is an essential part of science, then the theorists can no longer do science at all.

One of my colleagues made an interesting point: in the thought experiment, the theorists can’t predict new behaviors of reality. But they can predict new behaviors of the code.

Even when we have the right theory to describe the world, we can’t always calculate its consequences. Often we’re stuck in the same position as the theorists in the thought experiment, trying to understand the output of a theory that might as well be a black box. Increasingly, we are employing a kind of “experimental theoretical physics”. We try to predict the result of new calculations, just as experimentalists try to predict the result of new experiments.

This experimental approach seems to be a genuine cultural difference between physics and mathematics. There is such a thing as experimental mathematics, to be clear. And while mathematicians prefer proof, they’re not averse to working from a good conjecture. But when mathematicians calculate and conjecture, they still try to set a firm foundation. They’re precise about what they mean, and careful about what they imply.

“Experimental theoretical physics”, on the other hand, is much more like experimental physics itself. Physicists look for plausible patterns in the “data”, seeing if they make sense in some “physical” way. The conjectures aren’t always sharply posed, and the leaps of reasoning are often more reckless than the leaps of experimental mathematicians. We try to use intuition gleaned from a history of experiments on, and calculations about, the physical world.

There’s a real danger here, because mathematical formulas don’t behave like nature does. When we look at nature, we expect it to behave statistically. If we look at a large number of examples, we get more and more confident that they represent the behavior of the whole. This is sometimes dangerous in nature, but it’s even more dangerous in mathematics, because it’s often not clear what a good “sample” even is. Proving something is true “most of the time” is vastly different from proving it is true all of the time, especially when you’re looking at an infinity of possible examples. We can’t meet our favorite “five sigma” level of statistical confidence, or even know if we’re close.

At the same time, experimental theoretical physics has real power. Experience may be a bad guide to mathematics, but it’s a better guide to the mathematics that specifically shows up in physics. And in practice, our recklessness can accomplish great things, uncovering behaviors mathematicians would never have found by themselves.

The key is to always keep in mind that the two fields are different. “Experimental theoretical physics” isn’t mathematics, and it isn’t pretending to be, any more than experimental physics is pretending to be theoretical physics. We’re gathering data and advancing tentative explanations, but we’re fully aware that they may not hold up when examined with full rigor. We want to inspire, to raise questions and get people to think about the principles that govern the messy physical theories we use to describe our world. Experimental physics, theoretical physics, and mathematics are all part of a shared ecosystem, and each has its role to play.

# Things I’d Like to Know More About

This is an accountability post, of sorts.

As a kid, I wanted to know everything. Eventually, I realized this was a little unrealistic. Doomed to know some things and not others, I picked physics as a kind of triage. Other fields I could learn as an outsider: not well enough to compete with the experts, but enough to at least appreciate what they were doing. After watching a few string theory documentaries, I realized this wasn’t the case for physics: if I was going to ever understand what those string theorists were up to, I would have to go to grad school in string theory.

Over time, this goal lost focus. I’ve become a very specialized creature, an “amplitudeologist”. I didn’t have time or energy for my old questions. In an irony that will surprise no-one, a career as a physicist doesn’t leave much time for curiosity about physics.

One of the great things about this blog is how you guys remind me of those old questions, bringing me out of my overspecialized comfort zone. In that spirit, in this post I’m going to list a few things in physics that I really want to understand better. The idea is to make a public commitment: within a year, I want to understand one of these topics at least well enough to write a decent blog post on it.

Wilsonian Quantum Field Theory:

When you first learn quantum field theory as a physicist, you learn how unsightly infinite results get covered up via an ad-hoc-looking process called renormalization. Eventually you learn a more modern perspective, that these infinite results show up because we’re ignorant of the complete theory at high energies. You learn that you can think of theories at a particular scale, and characterize them by what happens when you “zoom” in and out, in an approach codified by the physicist Kenneth Wilson.

While I understand the basics of Wilson’s approach, the courses I took in grad school skipped the deeper implications. This includes the idea of theories that are defined at all energies, “flowing” from an otherwise scale-invariant theory perturbed with extra pieces. Other physicists are much more comfortable thinking in these terms, and the topic is important for quite a few deep questions, including what it means to properly define a theory and where laws of nature “live”. If I’m going to have an informed opinion on any of those topics, I’ll need to go back and learn the Wilsonian approach properly.

Wormholes:

If you’re a fan of science fiction, you probably know that wormholes are the most realistic option for faster-than-light travel, something that is at least allowed by the equations of general relativity. “Most realistic” isn’t the same as “realistic”, though. Opening a wormhole and keeping it stable requires some kind of “exotic matter”, and that matter needs to violate a set of restrictions, called “energy conditions”, that normal matter obeys. Some of these energy conditions are just conjectures, some we even know how to violate, while others are proven to hold for certain types of theories. Some energy conditions don’t rule out wormholes, but instead restrict their usefulness: you can have non-traversable wormholes (basically, two inescapable black holes that happen to meet in the middle), or traversable wormholes where the distance through the wormhole is always longer than the distance outside.

I’ve seen a few talks on this topic, but I’m still confused about the big picture: which conditions have been proven, what assumptions were needed, and what do they all imply? I haven’t found a publicly-accessible account that covers everything. I owe it to myself as a kid, not to mention everyone who’s a kid now, to get a satisfactory answer.

Quantum Foundations:

Quantum Foundations is a field that many physicists think is a waste of time. It deals with the questions that troubled Einstein and Bohr, questions about what quantum mechanics really means, or why the rules of quantum mechanics are the way they are. These tend to be quite philosophical questions, where it’s hard to tell if people are making progress or just arguing in circles.

I’m more optimistic about philosophy than most physicists, at least when it’s pursued with enough analytic rigor. I’d like to at least understand the leading arguments for different interpretations, what the constraints on interpretations are and the main loopholes. That way, if I end up concluding the field is a waste of time at least I’d be making an informed decision.

# The Black Box Theory of Everything

What is science? What makes a theory scientific?

There’s a picture we learn in high school. It’s not the whole story, certainly: philosophers of science have much more sophisticated notions. But for practicing scientists, it’s a picture that often sits in the back of our minds, informing what we do. Because of that, it’s worth examining in detail.

In the high school picture, scientific theories make predictions. Importantly, postdictions don’t count: if you “predict” something that already happened, it’s too easy to cheat and adjust your prediction. Also, your predictions must be different from those of other theories. If all you can do is explain the same results with different words you aren’t doing science, you’re doing “something else” (“metaphysics”, “religion”, “mathematics”…whatever the person you’re talking to wants to make fun of, but definitely not science).

Seems reasonable, right? Let’s try a thought experiment.

In the late 1950’s, the physics of protons and neutrons was still quite mysterious. They seemed to be part of a bewildering zoo of particles that no-one could properly explain. In the 60’s and 70’s the field started converging on the right explanation, from Gell-Mann’s eightfold way to the parton model to the full theory of quantum chromodynamics (QCD for short). Today we understand the theory well enough to package things into computer code: amplitudes programs like BlackHat for collisions of individual quarks, jet algorithms that describe how those quarks become signals in colliders, lattice QCD implemented on supercomputers for pretty much everything else.

Now imagine that you had a time machine, prodigious programming skills, and a grudge against 60’s era-physicists.

Suppose you wrote a computer program that combined the best of QCD in the modern world. BlackHat and more from the amplitudes side, the best jet algorithms and lattice QCD code, and more: a program that could reproduce any calculation in QCD that anyone can do today. Further, suppose you don’t care about silly things like making your code readable. Since I began the list above with BlackHat, we’ll call the combined box of different codes BlackBox.

Now suppose you went back in time, and told the bewildered scientists of the 50’s that nuclear physics was governed by a very complicated set of laws: the ones implemented in BlackBox.

Your “BlackBox theory” passes the high school test. Not only would it match all previous observations, it could make predictions for any experiment the scientists of the 50’s could devise. Up until the present day, your theory would match observations as well as…well as well as QCD does today.

(Let’s ignore for the moment that they didn’t have computers that could run this code in the 50’s. This is a thought experiment, we can fudge things a bit.)

Now suppose that one of those enterprising 60’s scientists, Gell-Mann or Feynman or the like, noticed a pattern. Maybe they got it from an experiment scattering electrons off of protons, maybe they saw it in BlackBox’s code. They notice that different parts of “BlackBox theory” run on related rules. Based on those rules, they suggest a deeper reality: protons are made of quarks!

But is this “quark theory” scientific?

“Quark theory” doesn’t make any new predictions. Anything you could predict with quarks, you could predict with BlackBox. According to the high school picture of science, for these 60’s scientists quarks wouldn’t be scientific: they would be “something else”, metaphysics or religion or mathematics.

And in practice? I doubt that many scientists would care.

“Quark theory” makes the same predictions as BlackBox theory, but I think most of us understand that it’s a better theory. It actually explains what’s going on. It takes different parts of BlackBox and unifies them into a simpler whole. And even without new predictions, that would be enough for the scientists in our thought experiment to accept it as science.

Why am I thinking about this? For two reasons:

First, I want to think about what happens when we get to a final theory, a “Theory of Everything”. It’s probably ridiculously arrogant to think we’re anywhere close to that yet, but nonetheless the question is on physicists’ minds more than it has been for most of history.

Right now, the Standard Model has many free parameters, numbers we can’t predict and must fix based on experiments. Suppose there are two options for a final theory: one that has a free parameter, and one that doesn’t. Once that one free parameter is fixed, both theories will match every test you could ever devise (they’re theories of everything, after all).

If we come up with both theories before testing that final parameter, then all is well. The theory with no free parameters will predict the result of that final experiment, the other theory won’t, so the theory without the extra parameter wins the high school test.

What if we do the experiment first, though?

If we do, then we’re in a strange situation. Our “prediction” of the one free parameter is now a “postdiction”. We’ve matched numbers, sure, but by the high school picture we aren’t doing science. Our theory, the same theory that was scientific if history went the other way, is now relegated to metaphysics/religion/mathematics.

I don’t know about you, but I’m uncomfortable with the idea that what is or is not science depends on historical chance. I don’t like the idea that we could be stuck with a theory that doesn’t explain everything, simply because our experimentalists were able to work a bit faster.

My second reason focuses on the here and now. You might think we have nothing like BlackBox on offer, no time travelers taunting us with poorly commented code. But we’ve always had the option of our own Black Box theory: experiment itself.

The Standard Model fixes some of its parameters from experimental results. You do a few experiments, and you can predict the results of all the others. But why stop there? Why not fix all of our parameters with experiments? Why not fix everything with experiments?

That’s the Black Box Theory of Everything. Each individual experiment you could possibly do gets its own parameter, describing the result of that experiment. You do the experiment, fix that parameter, then move on to the next experiment. Your theory will never be falsified, you will never be proven wrong. Sure, you never predict anything either, but that’s just an extreme case of what we have now, where the Standard Model can’t predict the mass of the Higgs.

What’s wrong with the Black Box Theory? (I trust we can all agree that it’s wrong.)

It’s not just that it can’t make predictions. You could make it a Black Box All But One Theory instead, that predicts one experiment and takes every other experiment as input. You could even make a Black Box Except the Standard Model Theory, that predicts everything we can predict now and just leaves out everything we’re still confused by.

The Black Box Theory is wrong because the high school picture of what counts as science is wrong. The high school picture is a useful guide, it’s a good rule of thumb, but it’s not the ultimate definition of science. And especially now, when we’re starting to ask questions about final theories and ultimate parameters, we can’t cling to the high school picture. We have to be willing to actually think, to listen to the philosophers and consider our own motivations, to figure out what, in the end, we actually mean by science.

# Changing the Question

I’ve recently been reading Why Does the World Exist?, a book by the journalist Jim Holt. In it he interviews a range of physicists and philosophers, asking each the question in the title. As the book goes on, he concludes that physicists can’t possibly give him the answer he’s looking for: even if physicists explain the entire universe from simple physical laws, they still would need to explain why those laws exist. A bit disappointed, he turns back to the philosophers.

Something about Holt’s account rubs me the wrong way. Yes, it’s true that physics can’t answer this kind of philosophical problem, at least not in a logically rigorous way. But I think we do have a chance of answering the question nonetheless…by eclipsing it with a better question.

How would that work? Let’s consider a historical example.

Does the Earth go around the Sun, or does the Sun go around the Earth? We learn in school that this is a solved question: Copernicus was right, the Earth goes around the Sun.

The details are a bit more subtle, though. The Sun and the Earth both attract each other: while it is a good approximation to treat the Sun as fixed, in reality it and the Earth both move in elliptical orbits around the same focus (which is close to, but not exactly, the center of the Sun). Furthermore, this is all dependent on your choice of reference frame: if you wish you can choose coordinates in which the Earth stays still while the Sun moves.

So what stops a modern-day Tycho Brahe from arguing that the Sun and the stars and everything else orbit around the Earth?

The reason we aren’t still debating the Copernican versus the Tychonic system isn’t that we proved Copernicus right. Instead, we replaced the old question with a better one. We don’t actually care which object is the center of the universe. What we care about is whether we can make predictions, and what mathematical laws we need to do so. Newton’s law of universal gravitation lets us calculate the motion of the solar system. It’s easier to teach it by talking about the Earth going around the Sun, so we talk about it that way. The “philosophical” question, about the “center of the universe”, has been explained away by the more interesting practical question.

My suspicion is that other philosophical questions will be solved in this way. Maybe physicists can’t solve the ultimate philosophical question, of why the laws of physics are one way and not another. But if we can predict unexpected laws and match observations of the early universe, then we’re most of the way to making the question irrelevant. Similarly, perhaps neuroscientists will never truly solve the mystery of consciousness, at least the way philosophers frame it today. Nevertheless, if they can describe brains well enough to understand why we act like we’re conscious, if they have something in their explanation that looks sufficiently “consciousness-like”, then it won’t matter if they meet the philosophical requirements, people simply won’t care. The question will have been eaten by a more interesting question.

This can happen in physics by itself, without reference to philosophy. Indeed, it may happen again soon. In the New Yorker this week, Natalie Wolchover has an article in which she talks to Nima Arkani-Hamed about the search for better principles to describe the universe. In it, Nima talks about looking for a deep mathematical question that the laws of physics answer. Peter Woit has expressed confusion that Nima can both believe this and pursue various complicated, far-fetched, and at times frankly ugly ideas for new physics.

I think the way to reconcile these two perspectives is to know that Nima takes naturalness seriously. The naturalness argument in physics states that physics as we currently see it is “unnatural”, in particular, that we can’t get it cleanly from the kinds of physical theories we understand. If you accept the argument as stated, then you get driven down a rabbit hole of increasingly strange solutions: versions of supersymmetry that cleverly hide from all experiments, hundreds of copies of the Standard Model, or even a multiverse.

Taking naturalness seriously doesn’t just mean accepting the argument as stated though. It can also mean believing the argument is wrong, but wrong in an interesting way.

One interesting way naturalness could be wrong would be if our reductionist picture of the world, where the ultimate laws live on the smallest scales, breaks down. I’ve heard vague hints from physicists over the years that this might be the case, usually based on the way that gravity seems to mix small and large scales. (Wolchover’s article also hints at this.) In that case, you’d want to find not just a new physical theory, but a new question to ask, something that could eclipse the old question with something more interesting and powerful.

Nima’s search for better questions seems to drive most of his research now. But I don’t think he’s 100% certain that the old questions are wrong, so you can still occasionally see him talking about multiverses and the like.

Ultimately, we can’t predict when a new question will take over. It’s a mix of the social and the empirical, of new predictions and observations but also of which ideas are compelling and beautiful enough to get people to dismiss the old question as irrelevant. It feels like we’re due for another change…but we might not be, and even if we are it might be a long time coming.

# Underdetermination of Theory by Metaphor

Sometimes I explain science in unconventional ways. I’ll talk about quantum mechanics without ever using the word “measurement”, or write the action of the Standard Model in legos.

Whenever I do this, someone asks me why. Why use a weird, unfamiliar explanation? Why not just stick to the tried and true, metaphors that have been tested and honed in generations of popular science books?

It’s not that I have a problem with the popular explanations, most of the time. It’s that, even when the popular explanation does a fine job, there can be good reason to invent a new metaphor. To demonstrate my point, here’s a new metaphor to explain why:

In science, we sometimes talk about underdetermination of a theory by the data. We want to find a theory whose math matches the experimental results, but sometimes the experiments just don’t tell us enough. If multiple theories match the data, we say that the theory is underdetermined, and we go looking for more data to resolve the problem.

What if you’re not a scientist, though? Often, that means you hear about theories secondhand, from some science popularizer. You’re not hearing the full math of the theory, you’re not seeing the data. You’re hearing metaphors and putting together your own picture of the theory. Metaphors are your data, in some sense. And just as scientists can find their theories underdetermined by the experimental data, you can find them underdetermined by the metaphors.

This can happen if a metaphor is consistent with two very different interpretations. If you hear that time runs faster in lower gravity, maybe you picture space and time as curved…or maybe you think low gravity makes you skip ahead, so you end up in the “wrong timeline”. Even if the popularizer you heard it from was perfectly careful, you base your understanding of the theory on the metaphor, and you can end up with the wrong understanding.

In science, the only way out of underdetermination of a theory is new, independent data. In science popularization, it’s new, independent metaphors. New metaphors shake you out of your comfort zone. If you misunderstood the old metaphor, now you’ll try to fit that misunderstanding with the new metaphor too. Often, that won’t work: different metaphors lead to different misunderstandings. With enough different metaphors, your picture of the theory won’t be underdetermined anymore: there will be only one picture, one understanding, that’s consistent with every metaphor.

That’s why I experiment with metaphors, why I try new, weird explanations. I want to wake you up, to make sure you aren’t sticking to the wrong understanding. I want to give you more data to determine your theory.

# Epistemology, Not Metaphysics, Justifies Experiments

While I was visiting the IAS a few weeks back, they had a workshop on Quantum Information and Black Holes. I didn’t see many of the talks, but I did get to see Leonard Susskind talk about his new slogan, GR=QM.

For some time now, researchers have been uncovering deep connections between gravity and quantum mechanics. Juan Maldacena jump-started the field with the discovery of AdS/CFT, showing that theories that describe gravity in a particular curved space (Anti-de Sitter, or AdS) are equivalent to non-gravity quantum theories describing the boundary of that space (specifically, Conformal Field Theories, or CFTs). The two theories contain the same information and, with the right “dictionary”, describe the same physics: in our field’s vernacular, they’re dual. Since then, physicists have found broader similarities, situations where properties of quantum mechanics, like entanglement, are closely linked to properties of gravity theories. Maldacena’s ER=EPR may be the most publicized of these, a conjectured equivalence between Einstein-Rosen bridges (colloquially known as wormholes) and entangled pairs of particles (famously characterized by Einstein, Podolsky, and Rosen).

GR=QM is clearly a riff on ER=EPR, but Susskind is making a more radical claim. Based on these developments, including his own work on quantum complexity, Susskind is arguing that the right kind of quantum mechanical system automatically gives rise to quantum gravity. What’s more, he claims that these systems will be available, using quantum computers, within roughly a decade. Within ten years or so, we’ll be able to do quantum gravity experiments.

That sounds ridiculous, until you realize he’s talking about dual theories. What he’s imagining is not an experiment at the absurdly high energies necessary to test quantum gravity, but rather a low-energy quantum mechanics experiment that is equivalent, by something like AdS/CFT, to a quantum gravity experiment.

Most people would think of that as a simulation, not an actual test of quantum gravity. Susskind, though, spends quite a bit of time defending the claim that it really is gravity, that literally GR=QM. His description of clever experiments and overarching physical principles is aimed at piling on evidence for that particular claim.

What do I think? I don’t think it matters much.

The claim Susskind is making is one of metaphysics: the philosophy of which things do and do not “really” exist. Unlike many physicists, I think metaphysics is worth discussing, that there are philosophers who make real progress with it.

But ultimately, Susskind is proposing a set of experiments. And what justifies experiments isn’t metaphysics, it’s epistemology: not what’s “really there”, but what we can learn.

What can we learn from the sorts of experiments Susskind is proposing?

Let’s get this out of the way first: we can’t learn which theory describes quantum gravity in our own world.

That’s because every one of these experiments relies on setting up a quantum system with particular properties. Every time, you’re choosing the “boundary theory”, the quantum mechanical side of GR=QM. Either you choose a theory with a known gravity partner, and you know how the inside should behave, or you choose a theory with an unknown partner. Either way, you have no reason to expect the gravity side to resemble the world we live in.

Plenty of people would get suspicious of Susskind here, and accuse him of trying to mislead people. They’re imagining headlines, “Experiment Proves String Theory”, based on a system intentionally set up to have a string theory dual, a system that can’t actually tell us whether string theory describes the real world.

That’s not where I’m going with this.

The experiments that Susskind is describing can’t prove string theory. But we could still learn something from them.

For one, we could learn whether these pairs of theories really are equivalent. AdS/CFT, ER=EPR, these are conjectures. In some cases, they’re conjectures with very good evidence. But they haven’t been proven, so it’s still possible there’s a problem people overlooked. One of the nice things about experiments and simulations is that they’re very good at exposing problems that were overlooked.

For another, we could get a better idea of how gravity behaves in general. By simulating a wide range of theories, we could look for overarching traits, properties that are common to most gravitational theories. We wouldn’t be sure that those properties hold in our world…but with enough examples, we could get pretty confident. Hopefully, we’d stumble on things that gravity has to do, in order to be gravity.

Susskind is quite capable of making these kinds of arguments, vastly more so than I. So it frustrates me that every time I’ve seen him talk or write about this, he hasn’t. Instead, he keeps framing things in terms of metaphysics, whether quantum mechanics “really is” gravity, whether the experiment “really” explores a wormhole. If he wants to usher in a new age of quantum gravity experiments, not just as a buzzword but as real, useful research, then eventually he’s going to have to stop harping on metaphysics and start talking epistemology. I look forward to when that happens.

# Our Bargain

Sabine Hossenfelder has a blog post this week chastising particle physicists and cosmologists for following “upside-down Popper”, or assuming a theory is worth working on merely because it’s falsifiable. She describes her colleagues churning out one hypothesis after another, each tweaking an old idea just enough to make it falsifiable in the next experiment, without caring whether the hypothesis is actually likely to be true.

Sabine is much more of an expert in this area of physics (phenomenology) than I am, and I don’t presume to tell her she’s wrong about that community. But the problem she’s describing is part of something bigger, something that affects my part of physics as well.

There’s a core question we’d all like to answer: what should physicists work on? What criteria should guide us?

Falsifiability isn’t the whole story. The next obvious criterion is a sense of simplicity, of Occam’s Razor or mathematical elegance. Sabine has argued against the latter, which prompted a friend of mine to comment that between rejecting falsifiability and elegance, Sabine must want us to stop doing high-energy physics at all!

That’s more than a little unfair, though. I think Sabine has a reasonably clear criterion in mind. It’s the same criterion that most critics of the physics mainstream care about. It’s even the same criterion being used by the “other side”, the sort of people who criticize anything that’s not string/SUSY/inflation.

The criterion is quite a simple one: physics research should be productive. Anything we publish, anything we work on, should bring us closer to understanding the real world.

And before you object that this criterion is obvious, that it’s subjective, that it ignores the very real disagreements between the Sabines and the Luboses of the world…before any of that, please let me finish.

We can’t achieve this criterion. And we shouldn’t.

We can’t demand that all physics be productive without breaking a fundamental bargain, one we made when we accepted that science could be a career.

The Hunchback of Notre Science

It wasn’t always this way. Up until the nineteenth century, “scientist” was a hobby, not a job.

After Newton published his theory of gravity, he was famously accused by Robert Hooke of stealing the idea. There’s some controversy about this, but historians agree on a few points: that Hooke did write a letter to Newton suggesting a $1/r^2$ force law, and that Hooke, unlike Newton, never really worked out the law’s full consequences.

Why not? In part, because Hooke, unlike Newton, had a job.

Hooke was arguably the first person for whom science was a full-time source of income. As curator of experiments for the Royal Society, it was his responsibility to set up demonstrations for each Royal Society meeting. Later, he also handled correspondence for the Royal Society Journal. These responsibilities took up much of his time, and as a result, even if he was capable of following up on the consequences of $1/r^2$ he wouldn’t have had time to focus on it. That kind of calculation wasn’t what he was being paid for.

We’re better off than Hooke today. We still have our responsibilities, to journals and teaching and the like, at various stages of our careers. But in the centuries since Hooke expectations have changed, and real original research is no longer something we have to fit in our spare time. It’s now a central expectation of the job.

When scientific research became a career, we accepted a kind of bargain. On the positive side, you no longer have to be independently wealthy to contribute to science. More than that, the existence of professional scientists is the bedrock of technological civilization. With enough scientists around, we get modern medicine and the internet and space programs and the LHC, things that wouldn’t be possible in a world of rare wealthy geniuses.

We pay a price for that bargain, though. If science is a steady job, then it has to provide steady work. A scientist has to be able to go in, every day, and do science.

And the problem is, science doesn’t always work like that. There isn’t always something productive to work on. Even when there is, there isn’t always something productive for you to work on.

Sabine blames “upside-down Popper” on the current publish-or-perish environment in physics. If physics careers weren’t so cut-throat and the metrics they are judged by weren’t so flawed, then maybe people would have time to do slow, careful work on deeper topics rather than pumping out minimally falsifiable papers as fast as possible.

There’s a lot of truth to this, but I think at its core it’s a bit too optimistic. Each of us only has a certain amount of expertise, and sometimes that expertise just isn’t likely to be productive at the moment. Because science is a job, a person in that position can’t just go work at the Royal Mint like Newton did. (The modern-day equivalent would be working for Wall Street, but physicists rarely come back from that.) Instead, they keep doing what they know how to do, slowly branching out, until they’ve either learned something productive or their old topic becomes useful once more. You can think of it as a form of practice, where scientists keep their skills honed until they’re needed.

So if we slow down the rate of publication, if we create metrics for universities that let them hire based on the depth and importance of work and not just number of papers and citations, if we manage all of that then yes we will improve science a great deal. But Lisa Randall still won’t work on Haag’s theorem.

In the end, we’ll still have physicists working on topics that aren’t actually productive.

A physicist lazing about unproductively under an apple tree

So do we have to pay physicists to work on whatever they want, no matter how ridiculous?

No, I’m not saying that. We can’t expect everyone to do productive work all the time, but we can absolutely establish standards to make the work more likely to be productive.

Strange as it may sound, I think our standards for this are already quite good, or at least better than many other fields.

First, there’s falsifiability itself, or specifically our attitude towards it.

Physics’s obsession with falsifiability has one important benefit: it means that when someone proposes a new model of dark matter or inflation that they tweaked to be just beyond the current experiments, they don’t claim to know it’s true. They just claim it hasn’t been falsified yet.

This is quite different from what happens in biology and the social sciences. There, if someone tweaks their study to be just within statistical significance, people typically assume the study demonstrated something real. Doctors base treatments on it, and politicians base policy on it. Upside-down Popper has its flaws, but at least it’s never going to kill anybody, or put anyone in prison.

Admittedly, that’s a pretty low bar. Let’s try to set a higher one.

Moving past falsifiability, what about originality? We have very strong norms against publishing work that someone else has already done.

Ok, you (and probably Sabine) would object, isn’t that easy to get around? Aren’t all these Popper-flippers pretending to be original but really just following the same recipe each time, modifying their theory just enough to stay falsifiable?

To some extent. But if they were really following a recipe, you could beat them easily: just write the recipe down.

Physics progresses best when we can generalize, when we skip from case-by-case to understanding whole swaths of cases at once. Over time, there have been plenty of cases in which people have done that, where a number of fiddly hand-made models have been summarized in one parameter space. Once that happens, the rule of originality kicks in: now, no-one can propose another fiddly model like that again. It’s already covered.

As long as the recipe really is just a recipe, you can do this. You can write up what these people are doing in computer code, release the code, and then that’s that, they have to do something else. The problem is, most of the time it’s not really a recipe. It’s close enough to one that they can rely on it, close enough to one that they can get paper after paper when they need to…but it still requires just enough human involvement, just enough genuine originality, to be worth a paper.

The good news is that the range of “recipes” we can code up increases with time. Some spaces of theories we might never be able to describe in full generality (I’m glad there are people trying to do statistics on the string landscape, but good grief it looks quixotic). Some of the time though, we have a real chance of putting a neat little bow on a subject, labeled “no need to talk about this again”.

This emphasis on originality keeps the field moving. It means that despite our bargain, despite having to tolerate “practice” work as part of full-time physics jobs, we can still nudge people back towards productivity.

One final point: it’s possible you’re completely ok with the idea of physicists spending most of their time “practicing”, but just wish they wouldn’t make such a big deal about it. Maybe you can appreciate that “can I cook up a model where dark matter kills the dinosaurs” is an interesting intellectual exercise, but you don’t think it should be paraded in front of journalists as if it were actually solving a real problem.

In that case, I agree with you, at least up to a point. It is absolutely true that physics has a dysfunctional relationship with the media. We’re too used to describing whatever we’re working on as the most important thing in the universe, and journalists are convinced that’s the only way to get the public to pay attention. This is something we can and should make progress on. An increasing number of journalists are breaking from the trend and focusing not on covering the “next big thing”, but in telling stories about people. We should do all we can to promote those journalists, to spread their work over the hype, to encourage the kind of stories that treat “practice” as interesting puzzles pursued by interesting people, not the solution to the great mysteries of physics. I know that if I ever do anything newsworthy, there are some journalists I’d give the story to before any others.

At the same time, it’s important to understand that some of the dysfunction here isn’t unique to physics, or even to science. Deep down the reason nobody can admit that their physics is “practice” work is the same reason people at job interviews claim to love the company, the same reason college applicants have to tell stirring stories of hardship and couples spend tens of thousands on weddings. We live in a culture in which nothing can ever just be “ok”, in which admitting things are anything other than exceptional is akin to calling them worthless. It’s an arms-race of exaggeration, and it goes far beyond physics.

(I should note that this “culture” may not be as universal as I think it is. If so, it’s possible its presence in physics is due to you guys letting too many of us Americans into the field.)

We made a bargain when we turned science into a career. We bought modernity, but the price we pay is subsidizing some amount of unproductive “practice” work. We can negotiate the terms of our bargain, and we should, tilting the field with incentives to get it closer to the truth. But we’ll never get rid of it entirely, because science is still done by people. And sometimes, despite what we’re willing to admit, people are just “ok”.


text:
## proxy variable [xkcd]

Posted in Books, Kids, Statistics with tags , , on August 7, 2022 by xi'an

## D65536 [xkcd]

Posted in Books, Kids with tags , , , on June 16, 2022 by xi'an

## health non-sense [xkcd]

Posted in Books, Kids, pictures, Statistics with tags , , , , , on June 5, 2022 by xi'an

## selection bias [xkcd]

Posted in Books, Kids, pictures, Statistics with tags , , on May 29, 2022 by xi'an

## information loss from the median

Posted in Books, Kids, Statistics with tags , , , , , , on April 19, 2022 by xi'an

An interesting side item from a X validated question about calculating the Fisher information for the Normal median (as an estimator of the mean). While this information is not available in closed form, it has a “nice” expression

$1+n\mathbb E[Z_{n/2:n}\varphi(Z_{n/2:n})]-n\mathbb E[Z_{n/2:n-1}\varphi(Z_{n/2:n-1})]+$
$\frac{n(n-1)}{n/2-2}\varphi(Z_{n/2-2:n-2})^2+\frac{n(n-1)}{n-n/2-1}\varphi(Z_{n/2:n-2})^2$

which can easily be approximated by simulation (much faster than by estimating the variance of said median). This shows that the median is about 1.57 less informative than the empirical mean. Bonus points for computing the information brought by the MAD statistic! (The information loss against the MLE is 2.69,  since the Monte Carlo ratio of their variances is 0.37.)


text:
We shall now consider the ‘geometrical’ series, whose general term is $$u_{n} = r^{n-1}$$. In this case $s_{n} = 1 + r + r^{2} + \dots + r^{n-1} = (1 – r^{n})/(1 – r),$ except in the special case in which $$r = 1$$, when $s_{n} = 1 + 1 + \dots + 1 = n.$ In the last case $$s_{n} \to +\infty$$. In the general case $$s_{n}$$ will tend to a limit if and only if $$r^{n}$$ does so. Referring to the results of § 72 we see that

the series $$1 + r + r^{2} + \dots$$ is convergent and has the sum $$1/(1 – r)$$ if and only if $$-1 < r < 1$$.

If $$r \geq 1$$, then $$s_{n} \geq n$$, and so $$s_{n} \to +\infty$$; the series diverges to $$+\infty$$. If $$r = -1$$, then $$s_{n} = 1$$ or $$s_{n} = 0$$ according as $$n$$ is odd or even: $$s_{n}$$ oscillates finitely. If $$r < -1$$, then $$s_{n}$$ oscillates infinitely. Thus, to sum up,

the series $$1 + r + r^{2} + \dots$$ diverges to $$+\infty$$ if $$r \geq 1$$, converges to $$1/(1 – r)$$ if $$-1 < r < 1$$, oscillates finitely if $$r = -1$$, and oscillates infinitely if $$r < -1$$.

Example XXIX

1. Recurring decimals. The commonest example of an infinite geometric series is given by an ordinary recurring decimal. Consider, for example, the decimal $$.217{\overline{13}}$$. This stands, according to the ordinary rules of arithmetic, for
\begin{align*}
\frac{2}{10} + \frac{1}{10^{2}} + \frac{7}{10^{3}} + \frac{1}{10^{4}} + \frac{3}{10^{5}} + \frac{1}{10^{6}} + \frac{3}{10^{7}} + \dots &= \frac{217}{1000} +\frac{ \frac{13}{10^{5}} }{1 – \frac{1}{10^{2}}}\\
&= \frac{2687}{12,375}.
\end{align*}
The reader should consider where and how any of the general theorems of § 77 have been used in this reduction.

2. Show that in general $.a_{1}a_{2}\dots a_{m} {\overline{\alpha_{1}\alpha_{2}\dots \alpha_{n}}} = \frac{a_{1}a_{2}\dots a_{m}\alpha_{1}\dots \alpha_{n} – a_{1}a_{2}\dots a_{n}} {99\dots 900\dots 0},$ the denominator containing $$n$$ $$9$$’s and $$m$$ $$0$$’s.

3. Show that a pure recurring decimal is always equal to a proper fraction whose denominator does not contain $$2$$ or $$5$$ as a factor.

4. A decimal with $$m$$ non-recurring and $$n$$ recurring decimal figures is equal to a proper fraction whose denominator is divisible by $$2^{m}$$ or $$5^{m}$$ but by no higher power of either.

5. The converses of Exs. 3, 4 are also true. Let $$r = p/q$$, and suppose first that $$q$$ is prime to $$10$$. If we divide all powers of $$10$$ by $$q$$ we can obtain at most $$q$$ different remainders. It is therefore possible to find two numbers $$n_{1}$$ and $$n_{2}$$, where $${n_{1} > n_{2}}$$, such that $$10^{n_{1}}$$ and $$10^{n_{2}}$$ give the same remainder. Hence $$10^{n_{1}} – 10^{n_{2}} = 10^{n_{2}}(10^{n_{1}-n_{2}} – 1)$$ is divisible by $$q$$, and so $$10^{n} – 1$$, where $$n = n_{1} – n_{2}$$, is divisible by $$q$$. Hence $$r$$ may be expressed in the form $$P/(10^{n} – 1)$$, or in the form $\frac{P}{10^{n}} + \frac{P}{10^{2n}} + \dots,$ i.e. as a pure recurring decimal with $$n$$ figures. If on the other hand $$q = 2^{\alpha}5^{\beta}Q$$, where $$Q$$ is prime to $$10$$, and $$m$$ is the greater of $$\alpha$$ and $$\beta$$, then $$10^{m}r$$ has a denominator prime to $$10$$, and is therefore expressible as the sum of an integer and a pure recurring decimal. But this is not true of $$10^{\mu}r$$, for any value of $$\mu$$ less than $$m$$; hence the decimal for $$r$$ has exactly $$m$$ non-recurring figures.

6. To the results of Exs. 2–5 we must add that of Ex. I. 3. Finally, if we observe that $.{\overline{9}} = \frac{9}{10} + \frac{9}{10^{2}} + \frac{9}{10^{3}} + \dots = 1,$ we see that every terminating decimal can also be expressed as a mixed recurring decimal whose recurring part is composed entirely of $$9$$’s. For example, $$.217 = .216{\overline{9}}$$. Thus every proper fraction can be expressed as a recurring decimal, and conversely.

7. Decimals in general. The expression of irrational numbers as non-recurring decimals. Any decimal, whether recurring or not, corresponds to a definite number between $$0$$ and $$1$$. For the decimal $$.a_{1}a_{2}a_{3}a_{4}\dots$$ stands for the series $\frac{a_{1}}{10} + \frac{a_{2}}{10^{2}} + \frac{a_{3}}{10^{3}} + \dots.$ Since all the digits $$a_{r}$$ are positive, the sum $$s_{n}$$ of the first $$n$$ terms of this series increases with $$n$$, and it is certainly not greater than $$.{\overline{9}}$$ or $$1$$. Hence $$s_{n}$$ tends to a limit between $$0$$ and $$1$$.

Moreover no two decimals can correspond to the same number (except in the special case noticed in Ex. 6). For suppose that $$.a_{1}a_{2}a_{3} \dots$$, $$.b_{1}b_{2}b_{3} \dots$$ are two decimals which agree as far as the figures $$a_{r-1}$$, $$b_{r-1}$$, while $$a_{r} > b_{r}$$. Then $$a_{r}\geq b_{r} + 1 > b_{r}.b_{r+1}b_{r+2} \dots$$ (unless $$b_{r+1}$$, $$b_{r+2}$$, … are all $$9$$’s), and so $.a_{1}a_{2} \dots a_{r}a_{r+1} \dots > .b_{1}b_{2} \dots b_{r}b_{r+1} \dots.$ It follows that the expression of a rational fraction as a recurring decimal (Exs. 2–6) is unique. It also follows that every decimal which does not recur represents some irrational number between $$0$$ and $$1$$. Conversely, any such number can be expressed as such a decimal. For it must lie in one of the intervals $0,\ 1/10;\quad 1/10,\ 2/10;\ \dots;\quad 9/10,\ 1.$ If it lies between $$r/10$$ and $$(r + 1)/10$$, then the first figure is $$r$$. By subdividing this interval into $$10$$ parts we can determine the second figure; and so on. But (Exs. 3, 4) the decimal cannot recur. Thus, for example, the decimal $$1.414\dots$$, obtained by the ordinary process for the extraction of $$\sqrt{2}$$, cannot recur.

8. The decimals $$.101\ 001\ 000\ 100\ 001\ 0\dots$$ and $$.202\ 002\ 000\ 200\ 002\ 0\dots$$, in which the number of zeros between two $$1$$’s or $$2$$’s increases by one at each stage, represent irrational numbers.

9. The decimal $$.111\ 010\ 100\ 010\ 10\dots$$, in which the $$n$$th figure is $$1$$ if $$n$$ is prime, and zero otherwise, represents an irrational number. [Since the number of primes is infinite the decimal does not terminate. Nor can it recur: for if it did we could determine $$m$$ and $$p$$ so that $$m$$, $$m + p$$, $$m + 2p$$, $$m + 3p$$, … are all prime numbers; and this is absurd, since the series includes $$m + mp$$.]1

Example XXX

1. The series $$r^{m} + r^{m+1} + \dots$$ is convergent if $$-1 < r < 1$$, and its sum is $$1/(1 – r) – 1 – r – \dots – r^{m-1}$$ (§ 77, (2)).

2. The series $$r^{m} + r^{m+1} + \dots$$ is convergent if $$-1 < r < 1$$, and its sum is $$r^{m}/(1 – r)$$ (§ 77, (4)). Verify that the results of Exs. 1 and 2 are in agreement.

3. Prove that the series $$1 + 2r + 2r^{2} + \dots$$ is convergent, and that its sum is $$(1 + r)/(1 – r)$$, ($$\alpha$$) by writing it in the form $$-1 + 2(1 + r + r^{2} + \dots)$$, ($$\beta$$) by writing it in the form $$1 + 2(r + r^{2} + \dots)$$, ($$\gamma$$) by adding the two series $$1 + r + r^{2} + \dots$$, $$r + r^{2} + \dots$$. In each case mention which of the theorems of § 77 are used in your proof.

4. Prove that the ‘arithmetic’ series $a + (a + b) + (a + 2b) + \dots$ is always divergent, unless both $$a$$ and $$b$$ are zero. Show that, if $$b$$ is not zero, the series diverges to $$+\infty$$ or to $$-\infty$$ according to the sign of $$b$$, while if $$b = 0$$ it diverges to $$+\infty$$ or $$-\infty$$ according to the sign of $$a$$.

5. What is the sum of the series $(1 – r) + (r – r^{2}) + (r^{2} – r^{3}) + \dots$ when the series is convergent? [The series converges only if $$-1 < r \leq 1$$. Its sum is $$1$$, except when $$r = 1$$, when its sum is $$0$$.]

6. Sum the series $r^{2} + \frac{r^{2}}{1 + r^{2}} + \frac{r^{2}}{(1 + r^{2})^{2}} + \dots.$ [The series is always convergent. Its sum is $$1 + r^{2}$$, except when $$r = 0$$, when its sum is $$0$$.]

7. If we assume that $$1 + r + r^{2} + \dots$$ is convergent then we can prove that its sum is $$1/(1 – r)$$ by means of § 77, (1) and (4). For if $$1 + r + r^{2} + \dots = s$$ then $s = 1 + r(1 + r^{2} + \dots) = 1 + rs.$

8. Sum the series $r + \frac{r}{1 + r} + \frac{r}{(1 + r)^{2}} + \dots$ when it is convergent. [The series is convergent if $$-1 < 1/(1 + r) < 1$$, i.e. if $$r < -2$$ or if $$r > 0$$, and its sum is $$1 + r$$. It is also convergent when $$r = 0$$, when its sum is $$0$$.]

9. Answer the same question for the series \begin{aligned} & r – \frac{r}{1 + r} + \frac{r}{(1 + r)^{2}} – \dots, && r + \frac{r}{1 – r} + \frac{r}{(1 – r)^{2}} + \dots,\\ & 1 – \frac{r}{1 + r} + \left(\frac{r}{1 + r}\right)^{2} – \dots, && 1 + \frac{r}{1 – r} + \left(\frac{r}{1 – r}\right)^{2} + \dots.\end{aligned}

10. Consider the convergence of the series \begin{aligned} & (1 + r) + (r^{2} + r^{3}) + \dots, && (1 + r + r^{2}) + (r^{3} + r^{4} + r^{5}) + \dots,\\ & 1 – 2r + r^{2} + r^{3} – 2r^{4} + r^{5} + \dots, && (1 – 2r + r^{2}) + (r^{3} – 2r^{4} + r^{5}) + \dots,\end{aligned} and find their sums when they are convergent.

11. If $$0 \leq a_{n} \leq 1$$ then the series $$a_{0} + a_{1}r + a_{2}r^{2} + \dots$$ is convergent for $$0 \leq r < 1$$, and its sum is not greater than $$1/(1 – r)$$.

12. If in addition the series $$a_{0} + a_{1} + a_{2} + \dots$$ is convergent, then the series $$a_{0} + a_{1}r + a_{2}r^{2} + \dots$$ is convergent for $$0 \leq r \leq 1$$, and its sum is not greater than the lesser of $$a_{0} + a_{1} + a_{2} + \dots$$ and $$1/(1 – r)$$.

13. The series $1 + \frac{1}{1} + \frac{1}{1\cdot2} + \frac{1}{1\cdot2\cdot3} + \dots$ is convergent. [For $$1/(1\cdot2 \dots n) \leq 1/2^{n-1}$$.]

The series $1 + \frac{1}{1\cdot2} + \frac{1}{1\cdot2\cdot3\cdot4} + \dots,\quad \frac{1}{1} + \frac{1}{1\cdot2\cdot3} + \frac{1}{1\cdot2\cdot3\cdot4\cdot5} + \dots$ are convergent.

15. The general harmonic series $\frac{1}{a} + \frac{1}{a + b} + \frac{1}{a + 2b} + \dots,$ where $$a$$ and $$b$$ are positive, diverges to $$+\infty$$.

[For $$u_{n} = 1/(a + nb) > 1/\{n(a + b)\}$$. Now compare with $$1 + \frac{1}{2} + \frac{1}{3} + \dots$$.]

16. Show that the series $(u_{0} – u_{1}) + (u_{1} – u_{2}) + (u_{2} – u_{3}) + \dots$ is convergent if and only if $$u_{n}$$ tends to a limit as $$n \to \infty$$.

17. If $$u_{1} + u_{2} + u_{3} + \dots$$ is divergent then so is any series formed by grouping the terms in brackets in any way to form new single terms.

18. Any series, formed by taking a selection of the terms of a convergent series of positive terms, is itself convergent.

1. All the results of Exs. XXIX may be extended, with suitable modifications, to decimals in any scale of notation. For a fuller discussion see Bromwich, Infinite Series, Appendix I.↩


text:
# Circular Motion - Quick Help Please!

1. Oct 18, 2005

### dekoi

Andy and Bella move in circular paths about a common point with the same constant angular velocity $$\omega$$. Bella's mass is half the mass of Andy. The distance, where Andy is from the centre of the circle, is twice the distance of Bella. Who of the two will experience the greater magnitude of the centripetal force, $$F_c$$?

The answer given is that they will experience the SAME force. However, I found otherwise.

Since $$F_c=m\omega^2R$$

$$F_a=m_a\omega^2R_a$$ and $$F_b=m_b\omega^2R_b$$

The ratios I obtained were: $$m_b=\frac{m_a}{2}$$ and $$R_b=\frac{R_a}{2}$$.

When I find the ratio, I get:
$$\frac{F_a}{F_b}=\frac{m_a\omega^2R_a}{m_b\omega^2R_b}=\frac{m_aR_a}{\frac{m_a}{2}\frac{R_a}{2}}$$

My end result will be the value, 4, which is not 1, which I am looking for in order for the forces to be equal.

Is there a problem with my method, or is the answer given the wrong answer?

2. Oct 18, 2005

### Staff: Mentor

I agree with your analysis. The answer is wrong. (Or someone messed up the problem statement.)

3. Oct 18, 2005

Thank you.


text:
# Apparent power generator-side

In an electric circuit, instantaneous power is the time rate of flow of energy past a given point of the circuit. In alternating current circuits, energy storage elements such as inductors and capacitors may result in periodic reversals of the direction of energy flow.

In order to feed a purely resistive load in a radial network with a given current through an underground line, it is necessary to inject a higher current at the source to compensate for cable capacitance with the difference being the capacitive current generated in the line.

Symbol
$S_G$
Unit
kVA
Formulae
 $\sqrt{3} U_o I_c$ three-phase system $U_o I_c$ two-phase system $U_o I_c$ single-phase system
Related
$I_c$
$U_o$
Used in
$P_L$