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# Browse by Subject "Engineering, Agricultural"

• (1985)
A laboratory study was conducted to investigate the Monod kinetic parameters associated with the design and operation of mesophilic digestion of swine manure containing the antibiotic chlortetracycline (CTC). The experimental ...

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• (1983)
A laboratory study was conducted to investigate the kinetic parameters important in the design and operation of thermophilic digestion of unmedicated swine manure. The experimental design was set up to test the effects of ...

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• (1993)
A knowledge-based machine vision system was developed for automatic corn quality inspection. This system consisted of a primitive feature extraction algorithm, several quality-related feature extraction algorithms, and ...

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• (1992)
A machine vision microscopy system (combination of video hardware and software and microscope for automated identification) was developed for classifying and counting microscopic objects in a Bacillus thuringiensis (Bt) ...

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• (1996)
A computer controlled machine vision sensing system for in vitro production of plant pigments was designed and implemented. The system consisted of a machine vision microscopic sensing subsystem and a computer controlled ...

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• (2002)
The research reported in this thesis addresses three areas, namely iron bioavailability, dust/odor reduction technologies, and dietary manipulation to reduce urine pH and swine odor. The first section, iron bioavailability, ...

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• (1970)

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• (2000)
The measured quantitative velocity data can be used to evaluate ventilation equipment and system design by manufacturers, optimize performance of ventilation equipment and systems, optimize environment of animals in different ...

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• (2007)
A field-scale bioreactor (6.1 m by 6.1 m) installed by researchers in the Agricultural and Biological Engineering Department of University of Illinois at Urbana-Champaign was selected for this study. The nitrate-N ...

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• (1991)
The purpose of this study was to nondestructively measure and analyze transient moisture profiles and associated structural changes during drying and cooling processes. Three yellow dent corn hybrids were measured during ...

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• (1963)

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• (1985)
The purpose of this study was to develop a microprocessor based controller capable of optimizing the drying process in a low temperature corn drying bin by controlling the drying fan operation. A procedure was developed ...

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• (1975)

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• (1996)
Reservoirs in east-central Illinois are subject to nitrate contamination due to the agricultural nature of their watersheds. Field tile systems provide direct links between leached nitrate and surface drainage systems. The ...

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• (1994)
A conceptual model, based upon the bicontinuum double porosity approach, has been developed to simulate water flow and reactive chemical transport in both the soil matrix and the macropore region. Flow of water in both ...

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• (1968)

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• (1994)
A series of experiments were conducted to test the feasibility and accuracy of using T$\sb1$ weighted magnetic resonance imaging to measure the temperature inside foods during heating. First, a steady state temperature ...

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• (1995)
Site-specific crop management aims to improve production efficiency by adjusting crop treatments, especially fertilizer and chemical application, to local conditions within the field. The implementation of spatially selective ...

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• (1988)
A natural-language interface (NLI) was developed in LISP for use with IBM-AT-compatible microcomputers to provide flexible access to computerized dairy records. NLI was designed to retrieve information from a dBASE III ...

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• (1989)
In-field sensing of soil organic matter content would be desirable to provide a control input for the variation of soil-applied herbicide application rates. Control based on organic matter content could eliminate overapplication ...

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text: References of "Nuclear Physics A"      in Complete repository Arts & humanities   Archaeology   Art & art history   Classical & oriental studies   History   Languages & linguistics   Literature   Performing arts   Philosophy & ethics   Religion & theology   Multidisciplinary, general & others Business & economic sciences   Accounting & auditing   Production, distribution & supply chain management   Finance   General management & organizational theory   Human resources management   Management information systems   Marketing   Strategy & innovation   Quantitative methods in economics & management   General economics & history of economic thought   International economics   Macroeconomics & monetary economics   Microeconomics   Economic systems & public economics   Social economics   Special economic topics (health, labor, transportation…)   Multidisciplinary, general & others Engineering, computing & technology   Aerospace & aeronautics engineering   Architecture   Chemical engineering   Civil engineering   Computer science   Electrical & electronics engineering   Energy   Geological, petroleum & mining engineering   Materials science & engineering   Mechanical engineering   Multidisciplinary, general & others Human health sciences   Alternative medicine   Anesthesia & intensive care   Cardiovascular & respiratory systems   Dentistry & oral medicine   Dermatology   Endocrinology, metabolism & nutrition   Forensic medicine   Gastroenterology & hepatology   General & internal medicine   Geriatrics   Hematology   Immunology & infectious disease   Laboratory medicine & medical technology   Neurology   Oncology   Ophthalmology   Orthopedics, rehabilitation & sports medicine   Otolaryngology   Pediatrics   Pharmacy, pharmacology & toxicology   Psychiatry   Public health, health care sciences & services   Radiology, nuclear medicine & imaging   Reproductive medicine (gynecology, andrology, obstetrics)   Rheumatology   Surgery   Urology & nephrology   Multidisciplinary, general & others Law, criminology & political science   Civil law   Criminal law & procedure   Criminology   Economic & commercial law   European & international law   Judicial law   Metalaw, Roman law, history of law & comparative law   Political science, public administration & international relations   Public law   Social law   Tax law   Multidisciplinary, general & others Life sciences   Agriculture & agronomy   Anatomy (cytology, histology, embryology...) & physiology   Animal production & animal husbandry   Aquatic sciences & oceanology   Biochemistry, biophysics & molecular biology   Biotechnology   Entomology & pest control   Environmental sciences & ecology   Food science   Genetics & genetic processes   Microbiology   Phytobiology (plant sciences, forestry, mycology...)   Veterinary medicine & animal health   Zoology   Multidisciplinary, general & others Physical, chemical, mathematical & earth Sciences   Chemistry   Earth sciences & physical geography   Mathematics   Physics   Space science, astronomy & astrophysics   Multidisciplinary, general & others Social & behavioral sciences, psychology   Animal psychology, ethology & psychobiology   Anthropology   Communication & mass media   Education & instruction   Human geography & demography   Library & information sciences   Neurosciences & behavior   Regional & inter-regional studies   Social work & social policy   Sociology & social sciences   Social, industrial & organizational psychology   Theoretical & cognitive psychology   Treatment & clinical psychology   Multidisciplinary, general & others     Showing results 1 to 20 of 67 1 2 3 4     SU(3) Clebsch-Gordan coefficients at large $N_c$Stancu, Floarea in Nuclear Physics A (2016), 945It is argued that several papers where SU(3) Clebsch-Gordan coefficients were calculated in order to describe properties of hadronic systems are, up to a phase convention, particular cases of analytic ... [more ▼]It is argued that several papers where SU(3) Clebsch-Gordan coefficients were calculated in order to describe properties of hadronic systems are, up to a phase convention, particular cases of analytic formulae derived by Hecht in 1965 in the context of nuclear physics. This is valid for irreducible representations with multiplicity one in the corresponding Clebsch-Gordan series. For multiplicity two, Hecht has proposed an alternative which can provide correct $1/N_c$ sub-leading orders in large $N_c$ studies. [less ▲]Detailed reference viewed: 31 (4 ULiège) Gauge symmetry and background independence: Should the proton spin decomposition be path independent?Lorce, Cédric in Nuclear Physics A (2014)Detailed reference viewed: 16 (2 ULiège) Extension of the Liège intranuclear cascade model at incident energies between 2 and 12 GeV. Aspects of pion production.Pedoux, S; Cugnon, Joseph in Nuclear Physics A (2011), 866Detailed reference viewed: 13 (1 ULiège) Production of Z+1 and A+1 Isotopes in Proton Induced Reactions on AZ NucleiCugnon, Joseph ; Aoust, Thierryin Nuclear Physics A (2009), 828Detailed reference viewed: 12 (1 ULiège) Quark transverse charge densities in the Delta(1232) from lattice QCDAlexandrou, Constantia; Korzec, Tomasz; Giannis, Koutsou et alin Nuclear Physics A (2009), A825We extend the formalism relating electromagnetic form factors to transverse quark charge densities in the light-front frame to the case of a spin-3/2 baryon and calculate these transverse densities for ... [more ▼]We extend the formalism relating electromagnetic form factors to transverse quark charge densities in the light-front frame to the case of a spin-3/2 baryon and calculate these transverse densities for the $\Delta (1232)$ isobar using lattice QCD. The transverse charge densities for a transversely polarized spin-3/2 particle are characterized by monopole, dipole, quadrupole, and octupole patterns representing the structure beyond that of a pure point-like spin-3/2 particle.We present lattice QCD results for the $\Delta$-isobar electromagnetic form factors for pion masses down to approximatively 350 MeV for three cases: quenched QCD, two-degenerate flavors of dynamicalWilson quarks, and three flavors of quarks using a mixed action that combines domain wall valence quarks and dynamical staggered sea quarks. We extract transverse quark charge densities from these lattice results and find that the $Delta$ is prolately deformed, as indicated by the fact that the quadrupole moment $G_{E2}(0)$ is larger than the value −3 characterizing a point particle and the fact that the transverse charge density in a $\Delta^+$ of maximal transverse spin projection is elongated along the axis of the spin. [less ▲]Detailed reference viewed: 27 (5 ULiège) A Review of the hard pomeron in soft diffractionCudell, Jean-René ; Lengyel, Alexander; Martynov, Evgenij et alin Nuclear Physics A (2005), 755We review the evidence for the presence of a hard singularity in soft forward amplitudes, and give an estimate of its trajectory and couplings.Detailed reference viewed: 54 (11 ULiège) A new model for production of fast light clusters in spallation reactionsBoudard, Alain; Cugnon, Joseph ; Leray, Sylvie et alin Nuclear Physics A (2004), 740(1-2), 195-210A model is proposed to describe emission of light charged clusters during the cascade stage in nucleon-induced spallation reactions. It consists in implementing a surface percolation procedure into the ... [more ▼]A model is proposed to describe emission of light charged clusters during the cascade stage in nucleon-induced spallation reactions. It consists in implementing a surface percolation procedure into the Liege intranuclear cascade (INCL4) model: when a nucleon is ready to leave the nuclear surface, it is allowed to drag along a cluster of nucleons, under some conditions of closeness in phase space. This possibility relies on the instantaneous dynamical phase space occupancy in the nuclear surface. The following clusters are considered: d, t, (3) He, (4) He. Good agreement is obtained with experimental data relative to heavy and medium-heavy targets at two different energies. It is shown that the implementation of light cluster emission in the cascade stage also improves our previous results for residue mass spectra. (C) 2004 Elsevier B.V. All rights reserved. [less ▲]Detailed reference viewed: 6 (1 ULiège) Three-body confinement force in a realistic constituent quark modelPapp, Z.; Stancu, Floarea in Nuclear Physics A (2003), 726(3-4), 327-338We show that in realistic constituent quark models based on a two-body confinement interaction color states appear in the middle of the experimentally known spectrum. To avoid this situation we implement ... [more ▼]We show that in realistic constituent quark models based on a two-body confinement interaction color states appear in the middle of the experimentally known spectrum. To avoid this situation we implement a three-body confinement interaction, introduced on an algebraic basis, into a semi relativistic version of the Goldstone boson exchange constituent quark model and by solving the Faddeev equations we show that this interaction can increase the gap between singlet and color states, such as the latter can be ignored and the known baryons can be described as simple q(3) systems. We analyze the effect of a Delta- and a Y-shape three-body interaction. (C) 2003 Elsevier B.V. All rights reserved. [less ▲]Detailed reference viewed: 16 (1 ULiège) Nucleon nucleon interaction in a chiral constituent quark modelBartz, Daniel ; Stancu, Floarea in Nuclear Physics A (2002), A699(1-2), 316-319We study the nucleon-nucleon interaction within a chiral constituent quark model where the hyperfine interaction is due to pseudoscalar meson exchange. We calculate the S-3(1) and S-1(0) phase shifts by ... [more ▼]We study the nucleon-nucleon interaction within a chiral constituent quark model where the hyperfine interaction is due to pseudoscalar meson exchange. We calculate the S-3(1) and S-1(0) phase shifts by using the resonating group method. Their behaviour clearly indicates the presence of a strong repulsive core at short distance. This is due to the spin-flavour symmetry of the interaction and to the quark interchange between the two interacting nucleons. We add a sigma-meson exchange quark-quark interaction which provides a medium range attraction necessary to describe the S-1(0) phase shift. We also explore the role of a tensor interaction at the quark level. [less ▲]Detailed reference viewed: 21 (5 ULiège) N N scattering phase shifts in a chiral constituent quark modelBartz, Daniel ; Stancu, Floarea in Nuclear Physics A (2001), A688We study the nucleon-nucleon interaction within a chiral constituent quark model which reproduces succesfully the baryon spectra. We calculate the $^3S_1$ and $^1S_0$ phase shifts by using the resonating ... [more ▼]We study the nucleon-nucleon interaction within a chiral constituent quark model which reproduces succesfully the baryon spectra. We calculate the $^3S_1$ and $^1S_0$ phase shifts by using the resonating group method. They clearly indicate the presence of a strong repulsive interaction at short distance, due to the spin-flavour symmetry of the quark-quark interaction and of the quark interchange between the two interacting nucleons. A $\sigma$-meson exchange quark-quark interaction, providing a medium-range attraction, helps to get closer to the experimental phase shifts. [less ▲]Detailed reference viewed: 16 (1 ULiège) The short-range baryon baryon interaction in a chiral constituent quark modelStancu, Floarea ; Glozman, Ya. L.in Nuclear Physics A (2001), A683The previous analysis of the short-range $NN$ repulsion originating from the Goldstone boson exchange hyperfine interaction between constituent quarks is revisited. We study in which respects the ... [more ▼]The previous analysis of the short-range $NN$ repulsion originating from the Goldstone boson exchange hyperfine interaction between constituent quarks is revisited. We study in which respects the repulsion depends on the radial form of the spin-spin quark-quark force. We show that while the radial form affects the structure of the 6Q wave function, the short-range repulsion in the $NN$ system persists in any case. We extend our analysis to other $YN$ and $YY$ (flavor octet-octet) systems and demonstrate that the flavor-spin hyperfine interaction implies a short-range repulsion in these B=2 systems as well. [less ▲]Detailed reference viewed: 20 (3 ULiège) Stability of strange quark matter in an effective chiral model with scale anomalyJaminon, Martine ; Van den Bossche, Brunoin Nuclear Physics A (2001), 686Stability of strange quark matter is investigated within a chiral model which implements the scale anomaly of QCD. As far as quark confinement is mimicked by a large value of the u-quark mass, the model ... [more ▼]Stability of strange quark matter is investigated within a chiral model which implements the scale anomaly of QCD. As far as quark confinement is mimicked by a large value of the u-quark mass, the model behaves in the chiral limit as a MIT bag model: it yields a stable system composed of quarks surrounded by the vacuum. As soon as finite current quark masses are taken into account, stability is however lost. [less ▲]Detailed reference viewed: 20 (2 ULiège) Strong decays of the glueball in a scaled effective LagrangianJaminon, Martine ; Mathot, Michel ; Van den Bossche, Brunoin Nuclear Physics A (2000), 662We calculate the scalar glueball decays into pipi, etaeta, etaeta' and KK within a modified version of the NJL model which implements the QCD trace anomaly. The glueball is assumed to be the f0(1500). It ... [more ▼]We calculate the scalar glueball decays into pipi, etaeta, etaeta' and KK within a modified version of the NJL model which implements the QCD trace anomaly. The glueball is assumed to be the f0(1500). It is coupled to the quarks due to its mixing with the scalar isoscalar mesons. The decay widths then contain a contribution coming from the triangle Feynman diagram. Moreover, they contain two additional contributions corresponding to the local decay of the glue component of the f0(1500): one comes from the process of regularization of the quark loop, the other from the interaction term a2chi2phgr2. Except for the etaeta' case, this local decay reduces the value of the width. The axial anomaly is introduced via a mass term for the eta'. As far as the lightest scalar glueball is identified with the f0(1500), the model cannot reproduce at the same time the dynamical properties of scalars and pseudoscalars. Since we do not include a model of confinement, we need to use a large quark mass (725 MeV) in our calculations. This leads to unphysical results for the two-pion decay width. A definitive test of our model awaits the introduction of a model of confinement, which we hope to include in a future work. [less ▲]Detailed reference viewed: 18 (3 ULiège) Two photon decay of the glueball and scalar isosclar mesons in a scaled NJL modelJaminon, Martine ; Van den Bossche, Brunoin Nuclear Physics A (1998), 636We use a modified version of the Nambu-Jona-Lasinio (NJL) model which implements the QCD trace anomaly to calculate the two photon decay width of the glueball (f0(1500)) and of the two scalar mesons (f0 ... [more ▼]We use a modified version of the Nambu-Jona-Lasinio (NJL) model which implements the QCD trace anomaly to calculate the two photon decay width of the glueball (f0(1500)) and of the two scalar mesons (f0(1370), fJ=0(1710)) to which it is mixed. We investigate the effect of the mixing over the coupling constants of the f0 states to the quarks and over the widths. We show that mass and phase space effects are crucial, at least in the NJL model, in determining the relative strength of the 2γ widths. [less ▲]Detailed reference viewed: 18 (2 ULiège) Nucleon and Deuteron Induced Spallation ReactionsCugnon, Joseph ; Volant, Claude; Vuillier, Stéphanein Nuclear Physics A (1997), 625Detailed reference viewed: 11 (1 ULiège) Improved Intranuclear Cascade Model for Nucleon-Nucleus InteractionsCugnon, Joseph ; Volant, Claude; Vuillier, Stéphanein Nuclear Physics A (1997), 620Detailed reference viewed: 9 (0 ULiège) Gluonic content of the scalar meson nonet in a scaled effective LagrangianJaminon, Martine ; Van den Bossche, Brunoin Nuclear Physics A (1997), 619A scaled SU(3) Nambu-Jona-Lasinio Lagrangian is used to compute the mass of the nine scalar mesons in the vacuum and the mass of the glueball. This chiral model provides a gluonic content to the scalar ... [more ▼]A scaled SU(3) Nambu-Jona-Lasinio Lagrangian is used to compute the mass of the nine scalar mesons in the vacuum and the mass of the glueball. This chiral model provides a gluonic content to the scalar mesons as well as a quark content to the glueball. It is shown that a suitable choice of the vacuum gluon condensate allows reproduction of the experimental masses of the scalar mesons except for K*0(1430). This choice corresponds to a weak coupling between the gluon and quark condensates, giving f0(1500) or fJ(1710) which is nearly a pure glueball. [less ▲]Detailed reference viewed: 13 (1 ULiège) Phase transition and thermodynamics of a hot and dense system in a scaled NJL modelCugnon, Joseph ; Jaminon, Martine ; Van den Bossche, Brunoin Nuclear Physics A (1996), 598he chiral phase transition of a hot and dense system of quarks is studied within a modified SU(3) NJL Lagrangian that implements the QCD scale anomaly. The u- and s-quark condensates can or can not feel ... [more ▼]he chiral phase transition of a hot and dense system of quarks is studied within a modified SU(3) NJL Lagrangian that implements the QCD scale anomaly. The u- and s-quark condensates can or can not feel the same chiral restoration depending on the considered region of the three-dimensional space (Tc, muuc, musc). The temperature behaviour of the pressure and the energy and entropy densities of the u- and s-quark system is investigated. At high temperature, the non-vanishing bare s-quark mass only modifies slightly the usual behaviour associated with an ideal quark gas. [less ▲]Detailed reference viewed: 10 (2 ULiège) Double Strangeness Production in Low Energy Antiproton-Nucleus AnnihilationCugnon, Joseph ; Dolgolenko, A.; Sibirtsev, A. et alin Nuclear Physics A (1995), 587Detailed reference viewed: 17 (0 ULiège) SU (3) scaled effective lagrangians for a hot and strange systemJaminon, Martine ; Van Den Bossche, Brunoin Nuclear Physics A (1995), 582We construct two effective lagrangians which reproduce the explicit flavor SU(3) symmetry breaking and the trace and axial anomalies of QCD. All analytical expressions are derived for a hot strange matter ... [more ▼]We construct two effective lagrangians which reproduce the explicit flavor SU(3) symmetry breaking and the trace and axial anomalies of QCD. All analytical expressions are derived for a hot strange matter but the results are only shown for zero baryonic density. We study the coupling of the quark condensates (u and s) to the gluon condensate. We also consider the temperature behavior of the pion and of the kaon masses. We show that the results crucially depend on the choice of the two free parameters of the model: the chiral transition can be of first or of second order; the coupling between the gluon and the quark condensates can be large or not; the meson masses can increase or decrease with temperature. The introduction of the QCD trace anomaly in the SU(3) NJL model kills the predictive character of the NJL. [less ▲]Detailed reference viewed: 19 (6 ULiège) 1 2 3 4

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# Definition of a function depending on a sequence

let $a_{n}$ is a given fixed sequence, say $a_{n}:=1/n$. I would like to define something like $$D_{j}:=\sum_{k=1}^{j}\frac{1}{j!}BellY[j,k,\{a_1,a_2,\dots,a_{j-k+1}\}].$$ Function BellY is implemented in Mathematica.

The problem is the variable number of inputs in BellY. How one can do that in Mathematica? Many thanks!

• welcome to MSE. There are a number of ways to do things in Mathematica. This site strongly encourages your own attempts (as this is the best way to learn). "Please code..." requests and similar is not looked on favourably. You have the raw materials and a built-in function, so dive in and have fun from now on. Here is one way to get you started: a[j_] := 1/j; d[j_] := With[{tab = a /@ Range[j], c = j!}, Total[BellY @@ {j, j - # + 1, tab[[1 ;; #]]} & /@ Range[j, 1, -1]]/ c]. – ubpdqn Sep 27 '15 at 10:54

Dj = Sum[1/Factorial[j] * BellY[j,k,q],{k,1,j}]


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## MacBook Pro 8,2 (Early 2011, 15” Unibody 2.3 GHz i7) – OS crashes randomly, after log in screen goes all white

I have a Macbook Pro, randomly started running into issues when logging in after start up. Occasionally will get the desktop to load but shortly thereafter the OS crashes leading to a screen with multiple colored lines which sometimes resolve after varying amounts of time. Following the crash and after re-boot/log-in the screen will go to all white.

After many of these crash sequences I booted into Recovery Mode and did a complete wipe of the harddrive with a fresh install of macOS (Sierra). I created a new user profile and logged in. All seemed well with normal use but after about 15 minutes of function as usual it went back to the same crashing sequence and white screen after log in.

Suspecting a hardware problem, I ran AHT (apple hardware test) and cycled 4 times with the Extended Testing which read “No trouble found.” for each cycle. Subsequent to this and suspecting a hard drive issues that is simply not being picked up by the AHT I booted again into Recovery mode to try running first aid on my hard drive and noticed that it is registering and being completely used with no free space (after a complete wipe and reinstall of macOS…it should be essentially empty).

I figure the complete wipe and re-install of mac OS would have solved any software related trouble that could be leading to this issue. That being said, I’m leaning toward one of three potential hardware issues being the source of my woes: hard drive, logic board or RAM. Right now the hard drive is my top suspicion but the clean cycles of AHT is confusing me.

Any ideas on where I can go from here to try and narrow down the source of the problem before I go trying to get any of the hardware replaced?

## Why do I get a 110: Connection timed out error, white serving a flask app through nginx and uwsgi?

I am trying to serve a flask application using nginx and uwsgi, through an ubuntu docker container, while the host is also an ubuntu 18.04 OS.

This is the conf file for the nginx server, for which I have created a symbolic link in /etc/nginx/sites-enabled:

server {     listen 1611;     real_ip_header X-Forwarded-For;     set_real_ip_from 127.0.0.1;     server_name localhost;      location / {         include uwsgi_params;         uwsgi_pass unix:/var/www/html/step_service/socket.sock;         uwsgi_modifier1 30;         } }

The uwsgi.ini’ file is as follows:

[uwsgi] base=/var/www/html/step_service app=app module=%(app) callable = app  home=%(base)/venv pythonpath=%(base) socket=%(base)/socket.sock chmod-socket=777  master=true processes=5 threads=5 die-on-term=true autostart=true autorestart=true harakiri=30 logto=/var/www/html/step_service/log/%n.log

The logs of uwsgi seem to indicate success:

 * Serving Flask app "app" (lazy loading)  * Environment: production    WARNING: Do not use the development server in a production environment.    Use a production WSGI server instead.  * Debug mode: off  * Running on http://0.0.0.0:5000/ (Press CTRL+C to quit)

The logs of nginx server (in particular error.log) is:

2019/04/18 16:23:30 [error] 6729#6729: *1 upstream timed out (110: Connection timed out) while reading response header from upstream, client: 172.17.0.1, server: localhost, request: "GET /rec/1/1 HTTP/1.1 ", upstream: "uwsgi://unix:/var/www/html/step_service/socket.sock", host: "172.17.0.2:1611" `

Any ideas would be more than welcome!

## Black screen with white cursor when trying to boot from Windows partition

I’ve been trying to install Windows 10 on my MacBook Pro (Late 2011) for a while now; digging on the internet, i ran with this tutorial on how to install Windows without a USB stick: No bootable device USB 2.0 MacBook Pro mid 2014

It Is a pretty well written tutorial, i tried to comment on the answer to ask my question but since i’m new here, i can’t do it.

After the step 8, when it’s time to reboot the computer and enter the Windows partition to install it, as soon as I hit Enter, a black screen with a white cursor on the top left corner appears and doesn’t go away. I had some trouble with the previous steps and I was able to solve them, but this one I can’t.

I really hope you can help me. Thank you!

## Number of different necklaces with 2 black and 6 white beads

This is not a home work question, I’m preparing for an entrance test. The number of different necklaces you can form with 2 black and 6 white beads is? My approach: We can place the white beads in the necklace in 1 way because they all are white. Then the black bead can again be placed anywhere in 1 way, once a black bead is placed it now acts like a reference, and I can place last black bead either to next of first black, or with a gap of 1,2,3 white beads, giving me 4 combinations as, wbbwwwww, wbwbwwww, wbwwbwww, wbwwwbww.

Is there any other better approach for this? I tried to follow this way, How many different necklaces can be formed with $6$ white and $5$ red beads? but I am getting fractional values, 7! /(6! *2! *2) why is it happening this way? Cant we use this formula logic in all cases?

## White screen after installing Lubuntu 18

I’ve an old laptop and decided to make use of it so I installed Lubuntu but after rebooting from installation I get a white screen with the black arrow of the mouse. Any fixes? New Linux user!! Laptop: intel celeron, 1.5 GB RAM

## [ Politics ] Open Question : Is Candace Owens a black white supremacist?

Its one thing to be out-spoken, brash, educated, and a freethinker. Its another to turn your back on your own people. Not only turn your back but support those who oppress your own people who are less fortunate than you. dear Republicans, you dont gain support from black folk, by promoting an Uncle Tom. You need to find a leader in the black community who speaks to the people in their language and can make them see your truth. Thats what the Dems do and how we got Obama. You dont need someone who says what you say…but just has a different skin tone than you. Its still the same crap you spew, that doesnt resonnate with black folk.

## Ubuntu Bionic 18.04 flashing white line at top of onitor

This problem is visible with a window whose edge is dark and is placed at the top of the monitor.

The problem only appears on my external DisplayPort monitor. It doesn’t appear on the laptop’s own display or an HDMI display.

The DisplayPort monitor runs at 2560×1440 resolution and the HDMI and laptop display run at 1920×1080.

## How to find the estimator of a signal with additive white noise

We have to derivate the MAP estimation of a signal $$x(m)$$ observed in AWGN $$n(m)$$, resulting $$y(m) = x(m) + n(m)$$, supposing no zero mean in any process. I have done this:

To find the MAP estimator, we have to find $$x$$ that verifies: $$argmax[p(y/x)p(x)]$$ or similary: $$argmax[\log(p(y/x)) + \log(p(x))]$$

Where:

$$p(x) = \frac{1}{\sqrt{2\pi \sigma_x^2}} e^{-\dfrac{(x-\mu_x)^2}{2\sigma_x^2}}$$

$$p(y/x) = \frac{1}{\sqrt{2\pi (\sigma_x^2 + \sigma_n^2)}} e^{-\dfrac{(y-\mu_x – \mu_n)^2}{2(\sigma_x^2 + \sigma_n^2)}}$$

Thus, taking into account that $$y = x+n$$:

$$\dfrac{\partial log(p(y/x)p(x))}{\partial x} = 0 \rightarrow \dfrac{x-\mu_x}{\sigma_x^2} = – \dfrac{y-\mu_y-\mu_n}{\sigma_x^2 + \sigma_n^2}$$

And finally

$$x = \dfrac{\sigma_x^2}{\sigma_x^2 + \sigma_n^2}(\mu_n – y) + \mu_x \dfrac{2\sigma_x^2 + \sigma_n^2}{\sigma_x^2 + \sigma_n^2}$$

However, the solution should be:

$$x = \dfrac{\sigma_x^2}{\sigma_x^2 + \sigma_n^2}(y-\mu_n) + \dfrac{\sigma_n^2}{\sigma_x^2 + \sigma_n^2} \mu_x$$

And I don’t even know if the probability density functions of the beginning are correct, they sounded to me. For that, I’d like if you could explain me how to derivate mainly $$p(y/x)$$.

I hope someone can help me. Thank you for your responses.

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text:
Chosen plaintext vs Chosen ciphertext

What is the difference between chosen plaintext and chosen ciphertext attack? In both of these adversary has access to paintext-ciphertext pairs.Then where lies the difference?

The difference is how the plaintext-ciphertext pairs that the attacker has access to are generated.

• In a chosen plaintext attack, the attacker chooses some plaintext and is handed the corresponding ciphertext. In other words, the attacker may encrypt arbitrary messages.
• In a chosen ciphertext attack, the attacker can additionally (a chosen ciphertext attack is usually understood to subsume a chosen plaintext attack) choose some ciphertext and is handed the corresponding plaintext. In other words, the attacker may encrypt and decrypt arbitrary messages.

(Note: usually, additional restrictions on the permitted messages are posed in a particular security game to make it "fair", since some notions of security are vacuous if the attacker can query really arbitrary messages.)

• Do we even see chosen ciphertext in practice? – Pacerier Feb 16 '15 at 23:15
• @Pacerier: Yes, we do. The POODLE attack on SSL is an example for this: en.wikipedia.org/wiki/POODLE and further openssl.org/~bodo/ssl-poodle.pdf – Nova Apr 6 '15 at 6:51
• But aren't both of those still the same? If the decrypted cipher text is presumably the same as the plain text, can't the chosen plaintext attack assume to also know the decrypted cipher text, and therefore have the same data available as the chosen ciphertext attack – Eddie May 23 '16 at 17:41
• Unless.. in a chosen ciphertext attack the attacker can modify the cipher text and "see if it decrypts" when ran through the decryption function? In which case, I can see the difference. – Eddie May 24 '16 at 17:40
• @yyyyyyy is chosen ciphertext a subset of known plaintext/ciphertext attacks? – Trey Feb 21 '18 at 19:46

In chosen plain-text attacks the adversary can obtain the encryption of plain-texts of its choice. In chosen cipher-text attacks can obtain the decryption of any cipher-text (Katz & Lindell, 2008). Technically a chosen-ciphertext should be called a chosen-cipher text and plain text attack (Ferguson, Schneier, & Kohno, 2010) however, that name would be too long. The difference is in chosen cipher text attacks you have access to both plain texts and cipher texts. The chosen cipher-text attacks is more powerful as a result of the manner in which it can find corresponding plain texts and cipher texts. There is a higher probability of finding the secret key with a chosen cipher text attack than a chosen plain-text attack.

• Should chosen-plaintext not also give you plain- and ciphertext? You chose the plaintext and get the appropiate ciphertext. – Nova Dec 26 '14 at 3:29
• No, Nova these are two different types of attacks with different emphases. There is a nuanced difference: in Chosen-Plaintext attacks you only choose plain texts to possibly find cipher texts. Chosen Cipher is actually more robust because you choose both plain texts and cipher texts as well. There is more freedom and ways to generate a cipher text/plain text statistical test, table or frequency chart. The book Cryptography Engineering discusses this in a straight forward fashion and Introduction to Modern Cryptography more abstractly. – Jacob E Mack Dec 26 '14 at 3:41
• I know that that are two different attacks, but as far as I understand your answer, in both attacks you get plaintext-ciphertext pairs, one with chosen plaintexts and one with chosen ciphertexts. – Nova Dec 26 '14 at 3:43
• Please see my edited reply above, sorry not clear at first Here is the exact quite from Cryptography Engineering on p. 32, pr. 5: "Obviously, the chosen-cipher text is more powerful than a chosen-plain text attack, as the attacker has more freedom." – Jacob E Mack Dec 26 '14 at 3:47
• Please see here with Thomas's reply, as he explains it wonderfully: crypto.stackexchange.com/questions/13274/… – Jacob E Mack Dec 26 '14 at 3:49

in Chosen plaintext , plaintext message chosen by cryptanalyst with its corresponding ciphertext but in chosen ciphertext chosen by cryptanalyst with its corresponding plaintext.


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# Results

## Chemical Group:Organophosphate Pesticides

• Measured in: Urine

### Project: Maternal and Infant Environmental Exposure Project (MIEEP)

95% Confidence Interval Selected Percentiles
Chemical measured Indicates exposure to Units Number of people tested Geometric mean Lower Upper 25th 50th 75th 90th Limit of Detection (LOD), wet-weight Notes
DMTP Dimethoate, malathion, methidathion, phosmet, and others μg/L 89 * * * <LOD <LOD <LOD <LOD 0.50

### Footnotes

# As of March 2013, PFBuS is no longer measured due to instrumental background interference.
**LOD changed during the time that samples were analyzed for this project.
*Geometric mean was not calculated because the chemical was found in less than 65% of the study group
*Geometric mean was not calculated because the chemical was found in less than 65% of the study group.
^Concentrations were adjusted for specific gravity using a reference value of 1.017 from NHANES 2007-2008.
§Summary statistics were based on 155 urine samples collected from 40 children.
ΔTwo samples were damaged during processing and could not be tested.
†Summary statistics were based on 138 urine samples collected from 38 adults.
‡Summary statistics were based on 150 urine samples collected from 40 adults.
♢Summary statistics were based on 168 urine samples collected from 40 children.


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# Eigenvalues of diagonal matrix with two rank-one perturbations

I would like to generalize this question to a diagonal matrix that has two rank-one updates which are both of a special form. In the previous question I asked why most of the eigenvalues of a diagonal $$n\times n$$ matrix D remain the same even if I perturb this matrix with a rank-one update $$bk^T$$, where b and k are n-dimensional vectors: $$D+bk^T$$ The eigenvalues of D are obviously its diagonal entries. Numerical evaluation showed that many of its eigenvalues remain the same even after adding the perturbation. The answer to this question gave a proof using Sylvester's determinant theorem and shows why rank-one updated diagonal matrices with eigenvalues of multiplicity k > 1 will have the exact same eigenvalues with multiplicity k-1. Instead of having a diagonal matrix with one rank-one update, I wondered whether a similar proof can be done for matrices that get two rank-one updates, i.e. $$D + bk^T + uv^T$$ where D is a $$n\times n$$ diagonal matrix, and b, k, u, v are n-dimensional vectors. Instead of arbitrary vectors as in the previous question, I take u and k to be of the form: $$(*,*,0,0,0,\cdots)$$ and v and b to be of the form: $$(0,0,*,*,*,\cdots)$$ The resulting matrix looks something like$$\begin{pmatrix} * & 0 & *&* & * & * & \cdots\\ 0 & * & *&* & * & * & \cdots\\ * & * & *&0 & 0 & 0 & \cdots\\ * & * & 0&* & 0 & 0 & \cdots\\ * & * & 0&0 & * & 0 & \cdots\\ * & * & 0&0 & 0 & * & \cdots\\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots \end{pmatrix}$$ where the diagonal elements come from D and the first two rows/columns come from the rank-one updates $$uv^T$$ and $$bk^T$$ respectively.

My numerical calculations show that in this case the eigenvalues of higher multiplicity also remain the same, at least partly. I tried to repeat the above proof from the previous question with two rank-one perturbations but I did not succeed. Can somebody help me out?

Edit: It would also be nice to get an analytical understanding about why numerically the first two eigenvalues of D are affected the most by this perturbation.

• Let's assume that $\lambda$ appears $k$ times on the diagonal of $D$. Then $D - \lambda I$ has an $n - k$-dimensional image and a $k$-dimensional kernel. But then $D - \lambda I + b k^T + u v^T$ has at most an $n - k + 2$-dimensional image so it has at least a $k - 2$-dimensional kernel. This shows that if $\lambda$ is an eigenvalue of $D$ of multiplicity $k \geq 3$ then $\lambda$ is also an eigenvalue of $D + b k^T + u v^T$ with multiplicity $k - 2$. – levap Feb 18 at 0:22

Suppose that we have a matrix, $$A$$, with an eigenvalue $$\lambda$$ of multiplicity $$k$$. Then we have the property that $$(A-\lambda I)v=0$$ where $$v$$ can be any combination of vectors $$v_i$$ for $$i$$ between $$1$$ and $$k$$, each of which also satisfy this equation and that are orthogonal to each other.
If we perform a rank-1 update to $$A$$, and then we now have $$(A+bc^T-\lambda I)(v+w)=0$$ for some $$w$$. Expanding our second equation and substituting in our first equation, we get $$(A+bc^T-\lambda I)w +[c^T v]b=0$$ where $$c^T v$$ is a scalar. If $$c^T v=0$$, then $$w=0$$ and there is no alteration to the eigenvector. Note, however, that $$v = \sum \alpha_i v_i$$, and so $$c^T v = \sum \alpha_i [c^T v_i]$$.
But you have $$k-1$$ degrees of freedom to ensure that $$c^T v=0$$, which means that, after the rank-1 update, eigenvalue $$\lambda$$ has multiplicity at least $$k-1$$.
But this didn't rely on $$A$$ being diagonal. Which means, after a rank-1 update, we can perform another rank-1 update - that is, we can perform a rank-1 update on $$A+bc^T$$. And the result is that the eigenvalue of multiplicity $$k-1$$ becomes an eigenvalue of multiplicity $$k-2$$.


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Question

# Particles of true solution are visible to naked eye.(A) True(B) False

Verified
128.7k+ views
Hint: Limit of vision of human naked eye is upto $10\mu m$, we cannot see further smaller particles. If the solution contains the particles that are in the range of size of naked human eye’s vision limit, then we can see them.

True solutions are those who have solute particles completely dissolved in the solution. In true solutions the particle sizes of solute are around 1 nm or ${10^{ - 9}}m$ .
A human naked eye cannot see particles smaller than $10\mu m$ means ${10^{ - 5}}m$.


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## Essential University Physics: Volume 1 (3rd Edition)

a) We use the equation for the depth to find: $h = \frac{p-p_0}{\rho g}= \frac{2.02\times 10^5 - 1.01\times 10^5}{1030\times 9.81}= 10 \ m$ b) We can now find the pressure: $= \frac{100}{10} \times 11 \times 10^ 3 = 110 \ MPa$


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# Cofactors of a 3×3 Matrix

## Definition

The minor of a three by three matrix with a sign is called the cofactor of an entry in a square of the order three.

### Introduction

Let’s consider a $3 \times 3$ matrix, denoted by $A$.

$A$ $\,=\,$ $\begin{bmatrix} e_{11} & e_{12} & e_{13} \\ e_{21} & e_{22} & e_{23} \\ e_{31} & e_{32} & e_{33} \\ \end{bmatrix}$

The cofactor of an element in a matrix of order $3$ is a product of the following factors.

1. The negative one raised to the power of sum of “the number of the row” and “the number of the column” of the respective entry.
2. The minor of the corresponding element.

$C_A$ $\,=\,$ $\begin{bmatrix} (-1)^{1+1} \times M_{11} & (-1)^{1+2} \times M_{12} & (-1)^{1+3} \times M_{13} \\ (-1)^{2+1} \times M_{21} & (-1)^{2+2} \times M_{22} & (-1)^{2+3} \times M_{23} \\ (-1)^{3+1} \times M_{31} & (-1)^{3+2} \times M_{32} & (-1)^{3+3} \times M_{33} \\ \end{bmatrix}$

$\therefore\,\,\,$ $C_A$ $\,=\,$ $\begin{bmatrix} M_{11} & -M_{12} & M_{13} \\ -M_{21} & M_{22} & -M_{23} \\ M_{31} & -M_{32} & M_{33} \\ \end{bmatrix}$

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# Sung-Jin Oh (KIAS)

The Analysis and PDE seminar will take place Monday, May 8, in 740 Evans Hall, from 16:10-17:00.

Title: Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data

Abstract: Black holes are perhaps the most celebrated predictions of general relativity. Miraculously, stationary black hole spacetimes arise as explicit (i.e., exact expression can be written down!) solutions to the (vacuum) Einstein equation. Looking at these explicit solutions leads to an intriguing observation: While the black hole exterior looks qualitatively similar, the structure of the interior, in particular the nature of the singularity’ inside the black hole, changes drastically depending on whether the black hole is spinning (Kerr) or not (Schwarzschild).

The topic of this talk is the strong cosmic censorship conjecture of R. Penrose, which is a proposed picture for what happens generically. In particular, I will present a recent work, joint with Jonathan Luk, where we establish a version of strong cosmic censorship for the Einstein-Maxwell-(real)-scalar-field system in spherical symmetry with two-ended asymptotically flat data, a toy model
that has been studied by physicists and mathematicians to understand issues connected to strong cosmic censorship in a simplified setting.

# Thomas Alazard (ENS Paris-Saclay)

The Analysis and PDE Seminar will take place on Monday, April 17, in room 740, Evans Hall, from 4:10-5:00 pm.

Title: Control of water waves

Abstract: Water waves are disturbances of the free surface of a liquid. They are, in general, produced by the immersion of a solid body or by impulsive pressures applied on the free surface. The question we discuss in this talk is the following: which waves can be generated by blowing on a localized portion of the free surface. Our main result asserts that one can generate any small amplitude, periodic in x, two-dimensional, gravity-capillary water waves. This is a result from control theory. More precisely, we prove the local exact controllability of the incompressible Euler equation with free surface. This is a joint work with Pietro Baldi and Daniel Han-Kwan.

# Camil Muscalu (Cornell)

The Analysis and PDE Seminar will take place on Monday, April 10, in room 740, Evans Hall, from 4:10-5:00 pm.

Title: The Helicoidal Method II

Abstract: The helicoidal method is a new, extremely efficient way, of proving multiple vector valued inequalities in harmonic analysis. About a month ago, we gave a talk at MSRI, in which we explained some consequences of this method, such as the proof of sparse domination results for various multilinear operators, and their multiple vector valued extensions.

The main task of the current talk will be different (hence the II from the title) as we plan to discuss the ideas that led us to the method. One specific application that we also plan to present, is the proof of mixed norm estimates for paraproducts on the bidisk, in the full possible range of Lebesgue spaces, answering completely an open question of Kenig, from the early 90’s. Joint work with Cristina BENEA.

# Steve Shkoller (UC Davis)

The Analysis and PDE seminar will take place on Monday, April 3rd, in Evans 740 from 16:10 to 17:00.

Title: Models for Rayleigh-Taylor mixing and interface turnover

Abstract: The instability of a heavy fluid layer supported by a light one is generally known as Rayleigh-Taylor (RT) instability. It can occur under gravity and, equivalently, under an acceleration of the fluid system in the direction toward the denser fluid. Whenever the pressure is higher in the lighter fluid, the differential acceleration causes the two fluids to mix.

The Euler equations serve as the basic mathematical model for RT instability and mixing between two fluids. This highly unstable system of conservation laws is both difficult to analyze (as it is ill-posed in the absence of surface tension and viscosity) and simulate; DNS of RT can be prohibitively expensive. In this talk, I will describe a novel framework to derive a hierarchy of asymptotic models that can be used to predict the location and shape of the RT interface as well as the mixing of the two fluids.

The models are derived in two very different asymptotic regimes. The first regime assumes that the fluid interface is a graph with size restrictions on the slope of the interface. The model PDE inherits the RT stability condition from the Euler equations, and in the stable regime, it is both locally and globally well-posed with precise asymptotic behavior that predicts nonlinear saturation for bubble growth. In the second asymptotic regime the interface can turnover, and there are no size restrictions on the amplitude or slope of the interface.

I will describe these models and show numerical simulations and comparisons with well-known RT experiments and simulations. I will then show results of fluid mixing, and discuss current work, advancing both modeling strategies. This is joint work with Rafa Granero.

# Hung Tran (University of Wisconsin-Madison)

The Analysis and PDE seminar will take place on Monday, March 20, in room 740, Evans hall, from 16:10 to 17:00.

Title: Homogenization: Beyond well-posedness theory.

Abstract: I will describe some recent progress on going beyond the well-posedness theory in homogenization of Hamilton-Jacobi equations. In particular, I will focus on the decomposition method to find the formula of the effective Hamiltonian in some situations. Joint work with Qian and Yu.

# Herbert Koch (University of Bonn)

The Analysis and PDE Seminar will take place on Monday, March 13, in room 740, Evans Hall, from 4:10-5:00 pm.

Title: Stationary solutions to the 2d Euler equation

Abstract: The two dimensional Euler equation has a large number of stationary solutions. Distribution functions of the vorticity are preserved under the flow.
I will explain a parametrization of Arnold stable stationary solutions by distribution functions of their vorticity. This is joint work with Antoine Chiffrut.

# Hajer Bahouri (Université Paris-Est Créteil)

The Analysis and PDE Seminar will take place on Monday, March 6, in room 740, Evans Hall, from 4:10-5:00 pm.

Title: Asymptotic analysis of Fourier transform on the Heisenberg group when the vertical frequency tends to 0

Abstract: In this joint work with Jean-Yves Chemin and Raphael Danchin, we propose a new approach of the Fourier transform on the Heisenberg group. The basic idea is to take advantage of Hermite functions so as to look at Fourier transform of integrable functions as mappings on the set $\tilde{\mathbb{H}}^d=\mathbb{N}^d\times\mathbb{N}^d\times\mathbb{R}\setminus\{0\}$ endowed with a suitable distance $\hat{d}$ (whereas with the standard viewpoint the Fourier transform is a one parameter family of bounded operators on $L^2(\mathbb{R}^d)$). We prove that the Fourier transform of integrable functions is uniformly continuous on $\tilde{\mathbb{H}}^d$ (for distance $\hat d$), which enables us to extend $\hat f_\mathbb{H}$ to the completion $\hat {\mathbb{H}}^d$ of $\tilde {\mathbb{H}}^d,$ and to get an explicit asymptotic description of the Fourier transform when the vertical’ frequency tends to $0.$ We expect our approach to be relevant for adapting to the Heisenberg framework a number of classical results for the $\mathbb{R}^n$ case that are based on Fourier analysis.

# Laurent Michel, Stanford and Université Nice

The Analysis and PDE Seminar will take place on Monday, February 13, in room 740, Evans Hall, from 4:10-5:00 pm.

Speaker: Laurent Michel

Title: On the small eigenvalues of the Witten Laplacian

Abstract: The Witten Laplacian, introduced (by E. Witten) in the early 80’s to give an analytic proof of the Morse inequalities, also models the dynamics of the over-damped Langevin equation. The understanding of the so-called metastable states goes through the description of its small eigenvalues. The first result in this direction was obtained in 2004 (Bovier-Gayrard-Klein, Helffer-Klein-Nier) under some generic assumptions on the landscape potential. In this talk, we present the approach of Helffer-Klein-Nier and show some recent progress to get rid of the generic assumption.

# Casey Jao (UC Berkeley)

The Analysis and PDE Seminar will take place on Monday, December 5, in room 740, Evans Hall, from 4:10-5:00 pm.

Speaker: Casey Jao

Title: Mass-critical inverse Strichartz theorems for 1d Schr\”{o}dinger operators

Abstract: I will discuss refined Strichartz estimates at $L^2$ regularity for a family of Schrödinger equations in one space dimension. Existing results rely on sophisticated Fourier analysis in spacetime and are limited to the translation-invariant equation $i\partial_t u = -\tfrac{1}{2} \Delta u$. Motivated by applications to mass-critical NLS, I will describe a physical space approach that applies in the presence of potentials including (but not limited to) the harmonic oscillator. This is joint work with Rowan Killip and Monica Visan.

# Jason Murphy (UC Berkeley)

The Analysis and PDE Seminar will take place on Monday, November 21th, in room 740, Evans Hall, from 4:10-5:00 pm.

Title: Scattering below the ground state for the radial focusing NLS

Abstract: We consider scattering below the ground state for the radial cubic focusing NLS in three dimensions. Holmer and Roudenko originally proved this via concentration compactness and a localized virial estimate. We present a simplified proof that avoids the use of concentration compactness, relying instead on the radial Sobolev embedding and a virial/Morawetz hybrid. This is joint work with Ben Dodson.


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# Reinforcement Learning - How are these state values in MRP calculated?

This is a question from the book an Introduction to RL, page 125, example 6.2.

The example compares the prediction abilities of TD(0) and constant $$\alpha$$ MC when applied to the below Markov reward process (the image is copied form the book):

In the above MRP, all episodes start in the state C then can go either left or right by one state in each step (with equal probability).

Episodes terminate either on the extreme left or the extreme right. When an episode terminates on the right, a reward of +1 occurs; all other rewards are zero. For example, a typical episode might consist of the following state-and-reward sequence: C, 0,B, 0, C, 0,D, 0, E, 1. Because this task is undiscounted, the true value of each state is the probability of terminating on the right if starting from that state.

The book mentions V(A)=1/6, V(B)=2/6, V(C)=3/6 , V(D)=4/6 and V(E)=5/6; could you please help me understand how these values were calculated? Thanks.

As it is such a small MRP, it is possible to solve it quickly and analytically using simultaneous equations based on the Bellman equation:

$$v(s) = \sum_{r,s'} p(r,s'|s)(r + v(s'))$$

and substituting in each state in turn. Using the variables $$a,b,c,d,e$$ to represent $$v(A), v(B), v(C), v(D), v(E)$$ makes this easier to read:

• $$a = \frac{1}{2}(0 + b)$$

• $$b = \frac{1}{2}(a+c)$$

• $$c = \frac{1}{2}(b+d)$$

• $$d = \frac{1}{2}(c+e)$$

• $$e = \frac{1}{2}(d+1)$$

It takes multiple substitutions to resolve any individual value, at least to start with. But it is possible to resolve these terms by repeated substitution of how many times $$a$$ they are, and then proceeding to the next equation getting each variable:

$$a = \frac{1}{2}(0 + b) \therefore b = 2a$$

$$b = \frac{1}{2}(a+c) \rightarrow 2a = \frac{1}{2}(a + c) \therefore c = 3a$$

$$c = \frac{1}{2}(b+d) \rightarrow 3a = \frac{1}{2}(2a + d) \therefore d = 4a$$

$$d = \frac{1}{2}(c+e) \rightarrow 4a = \frac{1}{2}(3a + e) \therefore e = 5a$$

$$e = \frac{1}{2}(d+1) \rightarrow 5a = \frac{1}{2}(4a+1) \therefore a = \frac{1}{6}$$

That last one resolves everything, and gives the expected answer. You can also see a very strong pattern here, which should intuitively hold for any length of one dimensional random walk with equal $$p=0.5$$ - there is a proof for that more general case that would void the need to work the substitutions in detail for each length, but that is more complex.

One other simple intuition: Each state value in turn is the mean of the two state values either side of it, without exception. That means taking any three values next to each other, they should be co-linear; the two higher and lower values with the mean between them. As this holds on all values with overlap, plotting the values in order should place all points all on the same line. That in turn means that there is a simple linear relationship between position in the random walk and the state value.


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Chapter 171

## Abstract

Abstract

1. Fibrinogen is a dimeric protein consisting of six polypeptide chains (αβγ)2 (MIM 134820, 134830, 134850) held together by disulfide bonds and folded in a trinodular structure where the globular nodules are connected by coiled coils. Thrombin converts fibrinogen to fibrin, which polymerizes into protofibrils through reciprocal half-staggered interactions. Protofibrils form macroscopic fibers through lateral aggregation and branch point formation. Crystallographic studies show that the polymerization pocket within the C-terminal region of the γ-chain is adjacent to but independent from the calcium-binding site. Fibrinogen is essential for platelet aggregation and wound healing. The genes for the constituent chains of fibrinogen are linked and are located on chromosome 4. Transcription of the fibrinogen genes is mediated by hepatocyte nuclear factor 1 and modulated by interleukin 6.

2. Genetic abnormalities of fibrinogen include afibrinogenemia (MIM 202400), hypofibrinogenemia, dysfibrinogenemia, and hyperfibrinogenemia. Afibrinogenemia is rare and is characterized by neonatal umbilical cord hemorrhage, intracranial and peritoneal bleeding, recurrent abortion, and autosomal recessive inheritance. Hypofibrinogenemia is characterized by fibrinogen levels below 100 mg/dl of plasma (normal 250–320 mg/dl) and can be inherited or acquired. The symptoms of hypofibrinogenemia are similar to but milder than those of afibrinogenemia. Dysfibrinogenemia is highly heterogeneous and may affect any one of the functional properties of fibrinogen, leading to manifestations that include hemorrhage, spontaneous abortion, and thrombosis. Most cases of dysfibrinogenemia are heterozygous for amino acid substitutions; homozygous occurrence is rare but known. Hyperfibrinogenemia is associated with an increased risk for myocardial infarction and stroke.

3. Factor XIII is a proenzyme for a plasma transglutaminase. It is converted to the active form, factor XIIIa, by thrombin in the presence of calcium ions. It catalyzes the formation of γ-glutamyl-ϵ-lysine bonds between fibrin monomers and between fibrin and α2-plasmin inhibitor. Factor XIII in plasma is a tetramer (A2B2) held together by noncovalent bonds. The A subunit contains the active site, and the B subunit is thought to stabilize the A subunit. The sequence around the active site is identical among all members of the transglutaminase family. The three-dimensional structure of the A subunit of factor XIII determined by x-ray crystallography demonstrated that it is composed of 5 distinct domains. The B subunit contains 10 tandem repeats, which have been designated as Sushi domains or GP-I structures. Homologous Sushi domains have been found in more than 30 other proteins/genes. The A subunit of plasma factor XIII is synthesized, in part, by hemopoietic cells, and is present in many tissues. The B subunit is synthesized in the liver.

4. The genes for the A and B subunits of factor XIII are localized at 6p24-p25 and 1q32-q32.1, respectively. Thus factor XIII deficiency is inherited as an autosomal recessive trait and is caused by the absence of either subunit. Recently, genetic defects have been identified at the DNA level in three patients with B-subunit deficiency (MIM 134580) and in 30 patients with A-subunit deficiency (MIM 134570). Their molecular and cellular bases also were explored in certain cases. This disease is characterized by delayed bleeding (“after bleeding”), though primary hemostasis is normal. Manifestations include neonatal bleeding from the umbilical cord, intracranial hemorrhage, and soft tissue hematomas. In addition, abnormal wound healing and recurrent spontaneous miscarriage are not rare. Infusion of factor XIII concentrates has been successful both for treatment of acute bleeding and for prophylaxis. Recombinant A subunit has been produced in yeast for clinical use.

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