text:
# E to the pi * i

1. Compute all the values of $$e^ {\pi i}$$, indicating clearly whether there is just one or many of them.

Trivially, exp(pi * i) = -1. However, we can also consider e to be the complex number z, and pi * i to be the complex number alpha. Then we get:

$$e^{\pi i} = z^{\alpha} = e^{\alpha log(z)} = e^{\alpha (Log |z| + i arg(z))} = e^{\pi i (Log |e| + i arg(e))} = e^{\pi i (1 + i2k\pi)} = e^{\pi i}e^{-2\pi^{2}k} = - e^{-2\pi^{2}k}$$
where k is an integer.

So what exactly is going on here? does exp(pi*i) = -1 or -exp(-2kpi^2)??

P.S. I hope all this tex doesn't mess up :(

Related Calculus and Beyond Homework Help News on Phys.org
something is wrong with LaTeX... it isn't displaying my tex right...

Mark44
Mentor
1. Compute all the values of $$e^ {\pi i}$$, indicating clearly whether there is just one or many of them.

Trivially, exp(pi * i) = -1. However, we can also consider e to be the complex number z, and pi * i to be the complex number alpha. Then we get:

$$e^{\pi i} = z^{\alpha} = e^{\alpha log(z)} = e^{\alpha (Log |z| + i arg(z))} = e^{\pi i (Log |e| + i arg(e))} = e^{\pi i (1 + i2k\pi)} = e^{\pi i}e^{-2\pi^{2}k} = - e^{-2\pi^{2}k}$$
where k is an integer.

So what exactly is going on here? does exp(pi*i) = -1 or -exp(-2kpi^2)??

P.S. I hope all this tex doesn't mess up :(

Is the complex exponential function invertible? (What is required for a function to have an inverse?)

Is the complex exponential function invertible? (What is required for a function to have an inverse?)
The function must be 1-1, right?

The function must be 1-1, right?
Correct. Does the complex exponential satisfy this?

Correct. Does the complex exponential satisfy this?
Sorry, I misread your first question. So, no, the complex exponential is not an invertible function. Where does my initial post break down then?

Sorry, I misread your first question. So, no, the complex exponential is not an invertible function. Where does my initial post break down then?
When you tried to invert it.


text:
# system of distinct representatives

Let $S=\left\{S_{1},S_{2},\dots S_{n}\right\}$ be a finite collection of finite sets. A system of distinct representatives, or SDR, of $S$ is a set

 $x_{1}\in S_{1},x_{2}\in S_{2},\dots x_{n}\in S_{n}$

such that

 $x_{i}\neq x_{j}\text{ whenever }i\neq j$

(i.e., each choice must be unique).

Title system of distinct representatives SystemOfDistinctRepresentatives 2013-03-22 12:35:11 2013-03-22 12:35:11 vampyr (22) vampyr (22) 4 vampyr (22) Definition msc 05D15 SDR

format: plain


text:
Preprint: Brownian Motion and Thermal Capacity

Davar Khoshnevisan and Yimin Xiao

Abstract. Let $W$ denote $d$-dimensional Brownian motion. We find an explicit formula for the essential supremum of Hausdorff dimension of $W(E)\cap F$, where $E\subset(0\,,\infty)$ and $F\subset\mathbf{R}^d$ are arbitrary nonrandom compact sets. Our formula is related intimately to the thermal capacity of Watson (1978). We prove also that when $d\ge 2$, our formula can be described in terms of the Hausdorff dimension of $E\times F$, where $E\times F$ is viewed as a subspace of space time.

Keywords. Brownian motion, thermal capacity, Euclidean and space-time Hausdorff dimension.

AMS Classification (2000) Primary: 60J65, 60G17; Secondary: 28A78, 28A80, 60G15, 60J45.

Support. Research supported in part by the the NSF grant DMS-1006903 (D.K.).

Pre/E-Prints. This paper is available in

 Davar Khoshnevisan Department of Mathematics University of Utah 155 S, 1400 E JWB 233 Salt Lake City, UT 84112-0090, U.S.A. davar@math.utah.edu Yimin Xiao Department of Statistics and Probability A-413 Wells Hall Michigan State University East Lansing, MI 48824, U.S.A. xiao@stt.msu.edu

Last Update: October 23, 2013
© 2011 - Davar Khoshnevisan & Yimn Xiao


text:
<< January 2018 >>

## Thursday, January 4, 2018

### Five Tables of XXS (Extra Extra Small) Art

Presentation | January 4 | 4-7 p.m. |  Berkeley Art Museum and Pacific Film Archive

This edition of Five Tables features tiny art—nothing larger than 5 x 5 inches: engravings by the Kleinmeister or Little Masters of the first half of the sixteenth century in Germany—Heinrich Aldegrever, Albrecht Altdorfer, and Hans Sebald Beham; delicate New Year’s woodblock prints by Shinsai and Shunman; Mieko Shiomi’s conceptual card game Fluxus Balance, and more!

## Friday, January 5, 2018

### Andean Studies Conference, Day 1: Institute for Andean Studies

Conference/Symposium | January 5 | 8:30 a.m.-5 p.m. | 160 Kroeber Hall

John Rick, President, Institute for Andean Studies

Institute of Andean Studies

The Institute of Andean Studies was the vision of John H. Rowe (1918–2004), who founded it in 1960.

$40 Early registration,$10 Student early registration, $60 Registration after Jan 1 and at the door,$20 Student registration after Jan 1 and at the door

or by calling 5106847930, or by emailing instituteofandeanstudies@gmail.com

### How to Write a Research Proposal Workshop

Workshop | January 5 | 2-3:30 p.m. | 9 Durant Hall

Leah Carroll

If you need to write a grant proposal, this workshop is for you! You'll get a headstart on defining your research question, developing a lit review and project plan, presenting your qualifications, and creating a realistic budget.

The workshop is open to all UC Berkeley students (undergraduate, graduate, and visiting scholars) regardless of academic discipline. It will be especially useful for...   More >

## Saturday, January 6, 2018

### Andean Studies Conference, Day 2: Institute for Andean Studies

Conference/Symposium | January 6 | 8:30 a.m.-10 p.m. | 160 Kroeber Hall

John Rick, President, Institute for Andean Studies

Institute of Andean Studies

The Institute of Andean Studies was the vision of John H. Rowe (1918–2004), who founded it in 1960.

$40 Early registration,$10 Student early registration, $60 Registration after Jan 1 and at the door,$20 Student registration after Jan 1 and at the door

or or by emailing instituteofandeanstudies@gmail.com

## Tuesday, January 9, 2018

### Genetically encoding new chemistries to read and write eukaryotic biology

Seminar | January 9 | 11 a.m.-12 p.m. | 120 Latimer Hall

Abhishek Chatterjee, Department of Chemistry, Boston College

College of Chemistry

Over the last decade, site-specific incorporation of non-canonical amino acids (ncAAs) into proteins in living cells has emerged as an enabling technology for biological research. Our group focuses on further development and application of this technology to understand and manipulate biological processes associated with mammalian cells. Two particular problems that we are currently addressing...   More >

## Thursday, January 11, 2018

### Introduction to Botanical Art Class with Catherine Watters

Workshop | January 11 – 12, 2018 every day | 10 a.m.-4 p.m. |  UC Botanical Garden

Botanical Garden

This two-day class will introduce you to the fascinating world of Botanical Art. Catherine Watters will teach you to observe, measure and draw plants in great detail and with botanical accuracy. Students will work with graphite, colored pencil and watercolors. All levels are welcome.

$190,$175 members

or by calling 510-664-9841, or by emailing gardenprograms@berkeley.edu

### From STEM to STEAM: Exploring E&O Opportunities with BAMPFA

Presentation | January 11 | 12-1:30 p.m. |  Berkeley Art Museum and Pacific Film Archive

Lynne Kimura, Collections Engagement Associate, Berkeley Art Museum and Pacific Film Archive (BAMPFA)

This session features a behind-the-scenes visit to the acclaimed Berkeley Art Museum, which curates many exhibits that draw connections between art and science.

Space is limited. RSVP is required for admission to the museum. RSVP by emailing Dan Zevin at dzevin@ssl.berkeley.edu by January 5.

### From STEM to STEAM: Exploring E&O Opportunities with BAMPFA

Presentation | January 11 | 12-1:30 p.m. | Berkeley Art Museum, 2155 Center Street

, Berkeley, CA 94720

Lynne Kimura, Collections Engagement Associate and Academic Liaison at the Berkeley Art Museum Pacific Film Archive (BAMPFA)., Berkeley Art Museum and Pacific Film Archive

This session features a behind-the-scenes visit to the acclaimed Berkeley Art Museum, which curates many exhibits that draw connections between art and science.

Space is limited. RSVP is required for admission to the museum. RSVP by emailing Dan Zevin at dzevin@ssl.berkeley.edu by January 5.

### EHS 201 Biosafety in Laboratories

Course | January 11 | 1:30-3:30 p.m. | 182 Dwinelle Hall | Note change in location

This training is required for anyone who is listed on a Biological Use Authorization (BUA) application form that is reviewed by the Committee for Laboratory and Environmental Biosafety (CLEB). A BUA is required for anyone working with recombinant DNA molecules, human clinical specimens or agents that may infect humans, plants or animals. This safety training will discuss the biosafety risk...   More >

## Friday, January 12, 2018

### 10th Annual CEND Symposium: Confronting Persistent Epidemics

Conference/Symposium | January 12 | 9 a.m.-6 p.m. | 245 Li Ka Shing Center

Stacey Schultz-Cherry, St. Jude Children's Research Hospital; Andrew Mehle, University of Wisconsin- Madison; Jonathan Yewdell, NIAID/DIR; Alfred Andama, Makerere University; Barbara Valent, Kansas State University; Nick Talbot, University of Exeter; Sophien Kamoun, The Sainsbury Laboratory; Thierry Diagana, Novartis Institutes for Biomedical Research; Kimberley Seed, University of California, Berkeley; Andy Camilli, Tufts University

### Introduction to Botanical Art Class with Catherine Watters

Workshop | January 11 – 12, 2018 every day | 10 a.m.-4 p.m. |  UC Botanical Garden

Botanical Garden

This two-day class will introduce you to the fascinating world of Botanical Art. Catherine Watters will teach you to observe, measure and draw plants in great detail and with botanical accuracy. Students will work with graphite, colored pencil and watercolors. All levels are welcome.

$190,$175 members

or by calling 510-664-9841, or by emailing gardenprograms@berkeley.edu

### MENA Salon: Protests in Iran

Workshop | January 12 | 3-4 p.m. | 340 Stephens Hall

As people across the world planned to ring in the New Year, cities across Iran erupted in the largest wave of protests the country has seen in almost a decade. The unrest, which has carried on into 2018, has prompted a number of debates. Who are the main actors? What are the protesters’ demands? Whom do they target? How are these demonstrations different from the 2009 Green Movement? Will they...   More >

## Saturday, January 13, 2018

### FAMILY PROGRAM: Trees and Birds

Workshop | January 13 | 10-11 a.m. |  UC Botanical Garden

Botanical Garden

Visit the botanical art exhibit "Celebrating Trees", take a tree walk, learn about nests and the winter birds of the Garden. Using materials from the garden, make a mini nest of your own to take home!

$15 Adult/Child,$12 Member Adult/Member Child

or by calling 510-664-9841, or by emailing gardenprograms@berkeley.edu

## Monday, January 15, 2018

### Analysis and PDE Seminar: Concentration of eigenfunctions: Averages and Sup-norms

Seminar | January 15 | 4-5 p.m. | 740 Evans Hall

Jeffrey Galkowski, Stanford University

Department of Mathematics

In this talk, we relate microlocal concentration of eigenfunctions to sup-norms and sub-manifold averages. In particular, we characterize the microlocal concentration of eigenfunctions with maximal sup-norm and average growth. We then exploit this characterization to derive geometric conditions under which maximal growth cannot occur. This talk is based on joint works with Yaiza Canzani and John...   More >

## Tuesday, January 16, 2018

### Evolution of Gliding in Lizards: Interview with Erik Sathe, Department of Integrative Biology

Presentation | January 16 | 9-9:30 a.m. | Barrows Hall, Radio broadcast, ON-AIR ONLY, 90.7 FM

Erik Sathe, PhD Candidate, Department of Integrative Biology; Tesla Monson, Department of Integrative Biology

KALX 90.7 FM

Join us for the first new episode of The Graduates this spring semester as we speak with biologist Erik Sathe about his work on lizard locomotion.

The Graduates, featuring graduate student research at Cal, is broadcast every other Tuesday on KALX 90.7 FM and online.

### New biological findings which were revealed by imaging studies based on chemical probes

Seminar | January 16 | 11 a.m.-12 p.m. | 120 Latimer Hall

Prof. Kazuya Kikuchi, Osaka University

College of Chemistry

One of the great challenges in the post-genome era is to clarify the biological significance of intracellular molecules directly in living cells. If we can visualize a molecule in action, it is possible to acquire biological information, which is unavailable if we deal with cell homogenates. One possible approach is to design and synthesize chemical probes that can convert biological information...   More >

### CRISPR Critters: Policy Choices for Non-Human Applications of Genome Editing

Seminar | January 16 | 12-1 p.m. | 115 Energy Biosciences Building

Alta Charo, Alta Charo Prof of Law and Bioethics, University of Wisconsin

### Development Lunch: "Socio-Economic Status and Attention Capture" and "Friend-Based Targeting"

Seminar | January 16 | 12:30-1:30 p.m. | 648 Evans Hall

Claire Duquennois; Matthew Olckers

Department of Economics

### 3-Manifold Seminar: Organizational meeting

Seminar | January 16 | 12:40-2 p.m. | 891 Evans Hall

Ian Agol, UC Berkeley

Department of Mathematics

We'll discuss some topics that I hope to consider this semester, including a continuation of the discussion of computational complexity of 3-manifold invariants from last semester, and Kronheimer-Mrowka's work on instanton homology for webs, as well as anything of interest to participants in the seminar.

### ISF 110 - Free Speech in the Public Sphere: An Interdisciplinary Approach

Course | January 16 – May 3, 2018 every Tuesday & Thursday | 2-3:30 p.m. | 102 Wurster Hall

In this spring 2018 class, we shall take up the nature of public speech from Socrates' public dissent to social media messaging today. The course reading will combine classic philosophical statements about the value of free, subversive and offensive speech; histories of the emergence of public spheres; and sociologies of technologically-mediated speech today.

Seminar | January 16 | 4-5 p.m. | 120 Latimer Hall

College of Chemistry

This presentation will first discuss the dynamic (and thermodynamics) of attachment of nanoparticles to fluid interfaces. We will look at the case where the nanoparticles are in dynamic equilibrium between the interface and a bulk phase and compare their adsorption to that of surfactants. We will demonstrate that the adsorption of nanoparticles competes with the attachment of amphiphilic ions...   More >

### Thematic Seminar: Number Theory: Random Groups from Generators and Relations

Seminar | January 16 | 4:10-5 p.m. | 740 Evans Hall

Melanie Matchett Wood, University of Wisconsin-Madison

Department of Mathematics

We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a universality theorem, an analog of the...   More >

### Davis Projects for Peace $10K award application deadline: 10k Grant Award Opportunity Deadline | January 16 | 5 p.m. | International House International House Projects for Peace is an initiative open to UC Berkeley undergrads to design grassroots projects for the summer of 2018 - anywhere in the world - which promote peace and address the root causes of conflict among parties. We encourage applicants to use their creativity to design projects and employ innovative techniques for engaging project participants in ways that focus on conflict... More > ## Wednesday, January 17, 2018 ### No Bioengineering Seminar today Seminar | January 17 | Stanley Hall Bioengineering (BioE) Seminars will begin on Wednesday, January 24. ### i4Y Child Marriage and Youth Empowerment Group Speaker Series: Balancing Reproductive Rights and Protections from Child Marriage: Insights from developmental science Seminar | January 17 | 11:30 a.m.-12:30 p.m. | 401 University Hall Ahna Suleiman, Center on the Developing Adolescent Innovations for Youth (i4Y) Balancing Reproductive Rights and Protections from Child Marriage - Insights from developmental science Policies aiming to protect children from early marriage can often be in direct tension with efforts to ensure adolescents' reproductive rights. Minimum age of marriage and the age at which young people can access contraceptive and reproductive health services vary widely globally and are... More > ### MVZ LUNCH SEMINAR: Jeffrey Kelly "Enroute migrant birds do not surf a green wave across the US" Seminar | January 17 | 12-1 p.m. | Valley Life Sciences Building, 3101 Grinnell-Miller Library Jeffrey Kelly Sponsored by DS421. MVZ Lunch is a graduate level seminar series (IB264) based on current and recent vertebrate research. The seminar meets every Wednesday from 12- 1pm in the Grinnell-Miller Library. ### [CANCELED] Plant and Microbial Biology Plant Seminar: "The Perfect Defense: Bacterial Persister Cell" Seminar | January 17 | 12-1 p.m. | 101 Barker Hall Kim Lewis, Northeastern University Our laboratory studies persister cells and uncultured bacteria. Persisters are dormant variants of regular cells which are tolerant to antibiotics and responsible for recalcitrance of biofilm infections. Using transcriptome analysis, cell sorting and whole genome sequencing we are identifying genes responsible for persister formation. ### Deportation Discretion: Tiered Influence, Minority Threat, and ‘Secure Communities’ Deportations: Juan Pedroza M.P.A, Stanford University Colloquium | January 17 | 12-1 p.m. | 2232 Piedmont, Seminar Room Juan Pedroza, PhD Candidate, Department of Sociology, Stanford University A lunch time talk and discussion session, featuring visiting and local scholars presenting their research on a wide range of topics of interest to demography. ### Getting Started in Undergraduate Research and Finding a Mentor Workshop Workshop | January 17 | 12-1 p.m. | 9 Durant Hall Leah Carroll, Haas Scholars Program Manager/Advisor, Office of Undergraduate Research and Scholarships Office of Undergraduate Research Getting Started in Undergraduate Research If you are thinking about getting involved in undergraduate research, this workshop is a great place to start! You will get a broad overview of the research opportunities available to undergraduates on campus, and suggestions on how to find them. We will also let you know about upcoming deadlines and eligibility requirements for some of... More > ### Aversion to Emotional Insurance: Costly Reluctance to Hedge Desired Outcomes Colloquium | January 17 | 12:10-1:15 p.m. | 5101 Tolman Hall Carey K. Morewedge, Professor, Boston University We examine whether people reduce the impact of negative outcomes through emotional hedging—betting against the occurrence of desired outcomes. We find substantial reluctance to bet against the success of preferred U.S. presidential candidates and Major League Baseball, National Football League, National Collegiate Athletic Association (NCAA) basketball, and NCAA hockey teams. This reluctance is... More > ### Last Stands? Art, Memory, and Public Space Panel Discussion | January 17 | 1-2:30 p.m. | Downtown Oakland Senior Center 200 Grand Avenue, Oakland, CA 94610 For decades, a painting of Custer’s defeat at Little Big Horn has been on display at the Veterans’ Memorial Building in downtown Oakland. Does the painting glorify genocidal 19-century domestic policies, depict the comeuppance of an arrogant US general at the hands of Lakota warriors... or both? More > ### Probabilistic Operator Algebra Seminar: Infinitely divisible distributions in free probability Seminar | January 17 | 2-4 p.m. | 736 Evans Hall Takahiro Hasebe, University of Hokkaido Department of Mathematics Free infinitely divisible distributions (FID) distributions were introduced by Voiculescu. Recently many classically infinitely divisible distributions have been shown to be FID too, the first highly nontrivial one being the normal distribution found by Belinschi, Bozejko, Lehner and Speicher in 2011. Also several subclasses of FID distributions have been introduced and studied. I will try to... More > ### Topology Seminar (Introductory Talk): Quasi-isometries: What are they and why do we care? Seminar | January 17 | 2-3 p.m. | 740 Evans Hall Ruth Charney, Brandeis University Department of Mathematics In this talk I will introduce the notion of a quasi-isometry and discuss the fundamental role it plays in geometric group theory. ### Number Theory Seminar: The cohomology of local Shimura varieties Seminar | January 17 | 3:30-5 p.m. | 748 Evans Hall Jared Weinstein, Boston University Department of Mathematics This is joint work with Tasho Kaletha. The local Langlands correspondence predicts that representations of a reductive group G over a p-adic field are related to Galois representations into the Langlands dual of G. A conjecture of Kottwitz (as generalized by Rapoport and Viehmann) asserts that this relationship appears in a precise way in the cohomology of "local Shimura varieties", which were... More > ### Electrolyte engineering toward a high-capacity, reversible lithium-oxygen battery/The Sudden Death Phenomena in Na-O2 Batteries Colloquium | January 17 | 4-6 p.m. | 180 Tan Hall Colin Burke, Ph.D. student in the McCloskey Group Jessica Nichols, Ph.D. student in the McCloskey Group ### Applied Math Seminar: A Variational Functional in Simulations of Statistical Mechanics Seminar | January 17 | 4-5 p.m. | 740 Evans Hall | Note change in location Yantao Wu, Princeton University Department of Mathematics In this talk, I advertise for a convex variational functional from statistical mechanics, which is particularly suitable for obtaining the free energy of high-dimensional order parameters from simulational sampling. In the numerical minimization of this variational functional, sampling difficulties related to ergodicity break-down are often alleviated. Two applications will be given. The first... More > ### From stopping times to “spotting” times : a new framework for multiple testing Seminar | January 17 | 4-5 p.m. | 1011 Evans Hall Aaditya Ramdas, UC Berkeley Department of Statistics Modern data science is often exploratory in nature, with hundreds or thousands of hypotheses being regularly tested on scientific datasets. The false discovery rate (FDR) has emerged as a dominant error metric in multiple hypothesis testing over the last two decades. I will argue that both (a) the FDR error metric, as well as (b) the current framework of multiple testing, where the scientist... More > ### Topology Seminar (Main Talk): Boundaries of groups Seminar | January 17 | 4-5 p.m. | 3 Evans Hall Ruth Charney, Brandeis University Department of Mathematics Boundaries of hyperbolic metric spaces have played an important role in the study of hyperbolic groups. We will discuss an analogous boundary for arbitrary finitely generated groups, called the Morse boundary, and present a recent theorem showing that in many cases, the Morse boundary determines the group up to quasi-isometry. (Joint work with M. Cordes and D. Murray) ### ERG Colloquium: Ted Parson: Climate Engineering: Benefits, Risks, Governance Challenges Colloquium | January 17 | 4-5:30 p.m. | 126 Barrows Hall Ted Parson, Professor of Environmental Law, UCLA Energy and Resources Group DESCRIPTION: Climate engineering (CE)—intentional, global-scale modification of the environment to offset some of the effects of elevated greenhouse gases—appears able to reduce climate-change risks beyond what is possible with mitigation and adaptation alone, including enabling integrated climate-response strategies that reduce risks in ways not otherwise achievable. ### Job Market Seminar: "Interpreting Signals in the Labor Market: Evidence from Medical Referrals" Seminar | January 17 | 4:10-5:30 p.m. | 648 Evans Hall Heather Sarsons, Harvard Economics Department of Economics Field(s): Labor, Behavioral, Development, Personnel Economics ## Thursday, January 18, 2018 ### Curators’ Talk: Lawrence Rinder and Kathy Geritz on Way Bay Panel Discussion | January 18 | 12 p.m. | Berkeley Art Museum and Pacific Film Archive Navigate the evocative installation of Way Bay with BAMPFA Director and Chief Curator Lawrence Rinder and Film Curator Kathy Geritz, two of the exhibition's cocurators. Rinder discusses associative, poetic groupings of artworks as well as individual selections, while Geritz illuminates some of the moving-image works on view. ### Seminar 217, Risk Management: Concrete examples of trend analyses and forward-looking modelling in Swiss Re's underwriting Seminar | January 18 | 12:30-2 p.m. | 1011 Evans Hall Speaker: Matthias Weber, Swiss Re - In insurance, underwriting performance is a function of exposures, losses relative to exposures and premiums relative to exposures. Getting losses and loss trends right (--> cost of goods sold) is critically important. A small estimation mistake typically has a large impact on the bottom line. - Swiss Re is determining loss relevant trends using advanced analytics, often in collaboration with... More > ### Job Market Seminar: "Bootstrap Inference for Propensity Score Matching" Seminar | January 18 | 12:40-2 p.m. | 648 Evans Hall | Note change in time Karun Adusumilli, London School of Economics and Political Science Department of Economics Field(s): Econometrics, Applied Econometrics ### ISF 110 - Free Speech in the Public Sphere: An Interdisciplinary Approach Course | January 16 – May 3, 2018 every Tuesday & Thursday | 2-3:30 p.m. | 102 Wurster Hall In this spring 2018 class, we shall take up the nature of public speech from Socrates' public dissent to social media messaging today. The course reading will combine classic philosophical statements about the value of free, subversive and offensive speech; histories of the emergence of public spheres; and sociologies of technologically-mediated speech today. ### How to Write a Research Proposal Workshop Workshop | January 18 | 3-4:30 p.m. | 9 Durant Hall Leah Carroll Office of Undergraduate Research If you need to write a grant proposal, this workshop is for you! You'll get a headstart on defining your research question, developing a lit review and project plan, presenting your qualifications, and creating a realistic budget. The workshop is open to all UC Berkeley students (undergraduate, graduate, and visiting scholars) regardless of academic discipline. It will be especially useful for... More > ### Thematic Seminar: Geometry: New Techniques for Zimmer's Conjecture Seminar | January 18 | 4:10-5 p.m. | 740 Evans Hall David Fisher, Indiana University Department of Mathematics Lattices in higher rank simple Lie groups are known to be extremely rigid. Examples of this are Margulis' superrigidity theorem, which shows they have very few linear represenations, and Margulis' arithmeticity theorem, which shows they are all constructed via number theory. Motivated by these and other results, in 1983 Zimmer made a number of conjectures about actions of these groups on compact... More > ### Employer Panel: How to Connect with Recruiters at Career Fairs for International Students Career Fair | January 18 | 6-7:30 p.m. | Career Center (2440 Bancroft Way), Blue and Gold Room The 2018 Spring Career Fair and many other career fairs are approaching quickly! Find more details in your Handshake and take these opportunities to demonstrate your passion, knowledge, and relevant experience for your dreamed opportunities. Employer representatives will share international students’ tips on how to prepare for a career fair, how to navigate through the companies and deliver... More > ## Friday, January 19, 2018 ### Qigong with Director Eric Siegel Workshop | January 19 | 10-11 a.m. | UC Botanical Garden Botanical Garden Join UCBG Director, Eric Siegel, for a morning practice in Qigong (pronounced cheegong), a form of meditative exercise with repeated movements, gently stretching the core and limbs and building body awareness. Free with Garden Admission ### Getting Started in Undergraduate Research and Finding a Mentor Workshop Workshop | January 19 | 11 a.m.-12 p.m. | 9 Durant Hall Leah Carroll, Haas Scholars Program Manager/Advisor, Office of Undergraduate Research and Scholarships Office of Undergraduate Research Getting Started in Undergraduate Research If you are thinking about getting involved in undergraduate research, this workshop is a great place to start! You will get a broad overview of the research opportunities available to undergraduates on campus, and suggestions on how to find them. We will also let you know about upcoming deadlines and eligibility requirements for some of... More > ### Cryo-EM Visualization of Microtubules to Understand Their Regulated Dynamics: Nano Seminar Series Seminar | January 19 | 1-2 p.m. | 390 Hearst Memorial Mining Building Prof. Eva Nogales, UC Berkeley / LBNL, Biochemistry Visualizing macromolecular assemblies, in different functional states, provides unique information on how they work in the cell and how they fail in the diseased state, and therefore can guide us in the design and improvement of therapies. But their small size and sensitivity to radiation makes visualization of biological molecules challenging and requires employment of highly specialized... More > ### MENA Salon: Austerity and Unrest in Tunisia Workshop | January 19 | 3-4 p.m. | 340 Stephens Hall Tunisia is often said to be the Arab Spring’s only success story, yet the new year has been marked by economic peril and political uncertainty. In this week’s MENA Salon we will discuss the recent unrest in Tunisia, and whether or not the government is fulfilling obligations set out under its post-Revolution constitution. Recommended reading available here: http://cmes.berkeley.edu/mena-salon/ ### How to Email a Professor to Get a Positive Response: Workshop Workshop | January 19 | 3-4 p.m. | 9 Durant Hall Leah Carroll Office of Undergraduate Research Do you need to email a professor you've never met before to ask for their help, but you don't know where to start? Have you ever written a long email to a professor, only to receive no response, or not the one you hoped? If so, this workshop is for you! We will discuss how to present yourself professionally over email to faculty and other professionals ... More > ### Making Web Archiving Work for Streaming Media: Archiving the Websites of Contemporary Young Composers Seminar | January 19 | 3:10-5 p.m. | 107 South Hall Howard Besser Information, School of Howard Besser is a professor of cinema studies and senior scientist for digital initiatives at New York University. ### Mathematics Department Colloquium: Complex multiplication, from Abel to Zagier Colloquium | January 19 | 3:10-4 p.m. | 748 Evans Hall | Note change in date, time, and location Jared Weinstein, Boston University Department of Mathematics According to Hilbert, the theory of complex multiplication, which brings together number theory and analysis, is not only the most beautiful part of mathematics but also of all science. "Complex multiplication" refers to a lattice in the complex numbers (or an elliptic curve) which admits endomorphisms by a ring larger than the integers. We will begin with Kronecker's "Jugendtraum" – the use of... More > ### Imagining Sculpture in China Colloquium | January 19 | 4-6 p.m. | 180 Doe Library Winnie Wong, Rhetoric, UC Berkeley Stanley Abe, Art, Art History, and Visual Studies, Duke University Center for Chinese Studies (CCS) There was no such thing as sculpture in China until the early twentieth century. Sculpture is a specifically European category of Fine Art which we apply to figural objects from many places. But sculpture did not exist in most of the world, certainly not in China, until the European term was applied on a global scale. The presentation will be a reflection about a book in progress—a picture... More > ### Metal-Organic Framework Liquids, Gels and Glasses Seminar | January 19 | 4-5 p.m. | 120 Latimer Hall College of Chemistry Crystalline solids dominate the field of metal−organic frameworks (MOFs),1 with access to the liquid and glass states of matter usually prohibited by relatively low temperatures of thermal decomposition. Recently, I have demonstrated the melting three dimensional MOFs belonging to the zeolitic imidazolate framework (ZIF) family, of chemical composition Zn(Im)2 (Im – C3H3N2].2 The mechanism... More > ### Job Market Seminar: "A Sieve-SMM Estimator for Dynamic Models" Seminar | January 19 | 4:10-5:30 p.m. | 648 Evans Hall Jean-Jacques Forneron, Columbia Economics Department of Economics Field(s): Econometrics, Macroeconometrics, Industrial Organization ### Thematic Seminar: Probability Theory: Rare Behavior in Models of Random Geometry Seminar | January 19 | 4:10-5 p.m. | 740 Evans Hall Shirshendu Ganguly, University of California, Berkeley Department of Mathematics Models of random geometry have long been investigated in contexts such as the internet, fluid flow in porous media, and interface dynamics in statistical physics. To develop a refined understanding of such models, one often needs to study not only typical fluctuation theory but also the realm of atypical events. In this talk we describe such a program for two classical models of random geometry:... More > ## Saturday, January 20, 2018 ### Weekend Workshop 2017-2018: Early Literacy Workshop | January 20 | 8:30 a.m.-12:30 p.m. | Tolman Hall Graduate School of Education Young children have fantastic imaginations and are amazing storytellers. Workshops will support primary classroom teachers to support students to understand how their oral composition skills connect to the writing process. Teachers will experience lessons that connect the creative aspects of writing and the mechanics of writing. ### Zapotec Natural Dye Workshop: with Porfirio Gutiérrez Workshop | January 20 | 10 a.m.-1 p.m. | Hearst Museum of Anthropology Porfirio Gutierrez Natural materials have been used to produce dyes and colorants throughout much of human history. in Oaxaca, the way of learning has been passed down from generation. Join master dyer and weaver Porfirio Gutiérrez to learn about the rich history of the craft in its cultural context, to make a range of richly colored dyes using natural colorants derived from the indigo, cochineal, and wild marigold... More > Must be 15 years of age and older to participate.$50 Workshop Registration

Tickets go on sale December 21. or or by emailing pahma-programs@berkeley.edu

## Sunday, January 21, 2018

### Lichen Dye Workshop

Workshop | January 21 | 10 a.m.-3 p.m. |  UC Botanical Garden

Botanical Garden

This class and workshop will provide an overview and history of lichen dyes followed by information on the methodologies of creating lichen dye baths. We will heat up some dyes and add fiber samples (provided). While the dye lichens are doing their work, Shelly will lead class participants on a walk in the surrounding area to look for lichens in the Garden. We will learn some common lichen...   More >

$85 /$75 Garden Members

Sold out.

## Monday, January 22, 2018

### Integration of guided experiential skill application into attention regulation training yields generalized improvements in cognitive functioning

Seminar | January 22 | 12-1:30 p.m. | 489 Minor Hall

Sahar Yousef, Silver Lab

Improvement of cognitive function is of great value to many aspects of society. However, identifying robust procedures for training cognitive processes in a generalizable way remains elusive. Here we present a novel attention regulation training paradigm that incorporates skill application in multiple learning environments. We hypothesized that our training procedure would enhance...   More >

### Combinatorics Seminar: Combinatorics of the Selberg integral

Seminar | January 22 | 12-1 p.m. | 939 Evans Hall

Jang Soo Kim, Sungkyunkwan University

Department of Mathematics

In 1944, Selberg evaluated a multivariate integral, which generalizes Euler's beta integral. In 1980, Askey conjectured a $q$-integral version of the the Selberg integral, which was proved independently by Habsieger and Kadell in 1988. In this talk, we focus on the combinatorial aspects of the Selberg integral. First, we review the following fact observed by Igor Pak: evaluating the Selberg...   More >

### Econ 235, Financial Economics: Job Market Seminar

Seminar | January 22 | 12:30-2 p.m. | C125 Haas School of Business

Anastassia Fedyk, Harvard

Department of Economics

Joint with Haas Finance Seminar

### Data Driven: Truckers and the New Workplace Surveillance

Colloquium | January 22 | 2-3:30 p.m. | 820 Barrows Hall

Karen Levy, Assistant Professor of Information Science, Associated Faculty at Cornell Law School, Cornell University

Social Science Matrix

This talk examines how electronic monitoring systems in the U.S. trucking industry are used to compel truckers' compliance with legal and organizational rules. New regulations will require truckers' time to be monitored by digital systems, hard-wired into the trucks themselves, which remove much of the flexibility on which truckers have historically relied.

### Probabilistic Operator Algebra Seminar: Boolean probability basics

Seminar | January 22 | 2-4 p.m. | 736 Evans Hall

Jorge Garza Vargas, UC Berkeley

Department of Mathematics

With the introduction of free independence by D.V. Voiculescu, it became clear that in the framework of non-commutative probability there are other notions of independence different than that of (classical) independence. In 1997, R. Speicher defined a notion of universal product for which he showed that there are three types of independence. In the category of unital algebras the tensor and free...   More >

### Differential Geometry Seminar: A polyhedron comparison theorem for 3-manifolds with positive scalar curvature

Seminar | January 22 | 2:10-3 p.m. | 939 Evans Hall

Chao Li, Stanford

Department of Mathematics

We establish a comparison theorem for polyhedra in 3-manifolds with nonnegative scalar curvature, answering affirmatively a dihedral rigidity conjecture by Gromov. For a large collection of polyhedra with interior non-negative scalar curvature and mean convex faces, we prove that the dihedral angles along its edges cannot be everywhere less or equal than those of the corresponding Euclidean...   More >

### Shuttle Catalysis – a Conceptual Blueprint for Reversible Functional Group Transfer

Seminar | January 22 | 3-4 p.m. | 775 Tan Hall

Prof. Bill Morandi, Max-Planck-Institut für Kohlenforschung

College of Chemistry

Catalytic reversible reactions, such as alkene metathesis and transfer hydrogenation, have had an auspicious impact on the molecular sciences. This presentation will describe our efforts to develop related “shuttle catalysis” reactions for the functionalization and defunctionalization of organic compounds.1-5 These reactions avoid the use of toxic reagents (e.g. HCN, CO) through the reversible...   More >

### Arithmetic Geometry and Number Theory RTG Seminar: The Brauer group of some algebraic stacks

Seminar | January 22 | 3:10-5 p.m. | 748 Evans Hall | Note change in date

Minseon Shin, UC Berkeley

Department of Mathematics

We will discuss recent developments in the computation of Brauer groups of some algebraic stacks, namely the moduli stack of elliptic curves $\mathscr M_{1,1}$ and torsion $\mathbb G_m$-gerbes.

Seminar Format: The seminar consists of two 50-minute talks, a pre-talk (3:10-4:00) and an advanced talk (4:10-5:00), with a 10-minute break (4:00-4:10) between them. The advanced talk is a regular formal...   More >

### Understanding rare events in models of statistical mechanics

Seminar | January 22 | 4-5 p.m. | 1011 Evans Hall

Shirshendu Ganguly, UC Berkeley

Department of Statistics

Statistical mechanics models are ubiquitous at the interface of probability theory, information
theory, and inference problems in high dimensions. In this talk, we will focus on
sparse networks, and polymer models on lattices. The study of rare behavior (large deviations)
is intimately related to the understanding of such models. In particular, we will
consider the rare events that a sparse...   More >

### Panel Discussion Honoring San Francisco Mayor Ed Lee

Panel Discussion | January 22 | 4-5:30 p.m. | Boalt Hall, School of Law, Room 105

Erin Dineen, Berkeley Law

Law, Boalt School of

The Bay Area and the Berkeley Law community lost one of its shining lights when Mayor Ed Lee passed away. Mayor Lee was a graduate of Berkeley Law (Class of 1978). His career was dedicated to public service and he made an enormous difference in so many people’s lives and in the Bay Area.

On Monday January 22nd, we will be holding a panel discussion about Ed Lee’s contributions and legacy. We...   More >

### Seminar 208, Microeconomic Theory: No Meeting

Seminar | January 22 | 4-5:30 p.m. | 639 Evans Hall

Department of Economics

### Understanding rare events in models of statistical mechanics

Seminar | January 22 | 4:10-5 p.m. | 1011 Evans Hall

Shirshendu Ganguly, UC Berkeley

Department of Statistics

Statistical mechanics models are ubiquitous at the interface of probability theory, information
theory, and inference problems in high dimensions. In this talk, we will focus on
sparse networks, and polymer models on lattices. The study of rare behavior (large deviations)
is intimately related to the understanding of such models. In particular, we will
consider the rare events that a sparse...   More >

### Thematic Seminar: Numerical Methods: Machine Learning at Facebook

Seminar | January 22 | 4:10-5 p.m. | 939 Evans Hall

Department of Mathematics

Machine intelligence for processing big data sets is big business. A mathematician's point of view has led to (1) effective large-scale principal component analysis and singular value decomposition, and (2) theoretical foundations for convolutional networks (convolutional networks underpin the recent revolution in artificial intelligence).

## Tuesday, January 23, 2018

### EHS 201 Biosafety in Laboratories

Course | January 23 | 9:30-11:30 a.m. | 177 Stanley Hall

This training is required for anyone who is listed on a Biological Use Authorization (BUA) application form that is reviewed by the Committee for Laboratory and Environmental Biosafety (CLEB). A BUA is required for anyone working with recombinant DNA molecules, human clinical specimens or agents that may infect humans, plants or animals. This safety training will discuss the biosafety risk...   More >

### Iron(III)-Catalyzed Carbonyl-Olefin Metathesis and Oxygen Atom Transfer

Seminar | January 23 | 11 a.m.-12 p.m. | 120 Latimer Hall

Corinna Schindler, Department of Chemistry, University of Michigan

College of Chemistry

The metathesis reaction between two unsaturated organic substrates is one of organic chemistry’s most powerful carbon-carbon bond forming reactions. The catalytic olefin-olefin metathesis reaction has led to profound developments in the synthesis of molecules relevant to the petroleum, materials and pharmaceutical industries. These reactions are characterized by their use of discrete
metal...   More >

### BSAC Technology Seminar - Single Crystal Diamond as a Material for Micro- and Nanosystems

Seminar | January 23 | 12-1 p.m. | 540 Cory Hall

The extraordinary properties of single crystal diamond provide great promise for nanosystems. Our group has developed methods to sculpture nanostructures into high purity monocrystalline diamond substrates grown by CVD. We combine reactive ion etching and multi-directional focused ion beam milling for the fabrication of freestanding optical disc resonators at the microscale.

by January 22.

### Development Lunch: "An egg for an egg and a bean for a bean? How production diversity determines dietary diversity of smallholder farmers in rural India" and "How do gendered perceptions of tasks affect labor market outcomes?"

Seminar | January 23 | 12:30-1:30 p.m. | 648 Evans Hall

Till Ludwig; Suanna Oh

Department of Economics

### Women on Africa's constitutional and supreme courts: When, where, and why?

Colloquium | January 23 | 12:30-2 p.m. | 223 Moses Hall

Alice Kang, Associate Professor, Political Science and Ethnic Studies, University of Nebraska-Lincoln

Center for African Studies

This is a meeting of the weekly colloquium for the Center for African Studies.

### 3-Manifold Seminar: Knottedness and Thurston norm in NP

Seminar | January 23 | 12:40-2 p.m. | 891 Evans Hall

Ian Agol, UC Berkeley

Department of Mathematics

We'll discuss a proof that knot recognition is in NP, using a certificate that encodes a sutured manifold hierarchy.

### Seminar 218, Psychology and Economics: "The Biases of Others: Projection Equilibrium in an Agency Setting"

Seminar | January 23 | 2-3:30 p.m. | 648 Evans Hall

Stephanie Wang, University of Pittsburgh

Department of Economics

### How to Write a Research Proposal Workshop

Workshop | January 23 | 2-3:30 p.m. | 9 Durant Hall

Leah Carroll

If you need to write a grant proposal, this workshop is for you! You'll get a headstart on defining your research question, developing a lit review and project plan, presenting your qualifications, and creating a realistic budget.

The workshop is open to all UC Berkeley students (undergraduate, graduate, and visiting scholars) regardless of academic discipline. It will be especially useful for...   More >

### ISF 110 - Free Speech in the Public Sphere: An Interdisciplinary Approach

Course | January 16 – May 3, 2018 every Tuesday & Thursday | 2-3:30 p.m. | 102 Wurster Hall

In this spring 2018 class, we shall take up the nature of public speech from Socrates' public dissent to social media messaging today. The course reading will combine classic philosophical statements about the value of free, subversive and offensive speech; histories of the emergence of public spheres; and sociologies of technologically-mediated speech today.

### RNA/Protein Liquids: Lighting up intracellular phase space

Seminar | January 23 | 3:30-4:30 p.m. | 100 Genetics & Plant Biology Building

Clifford Brangwynne, Princeton University

### Design Field Notes: Sara Cinnamon

Seminar | January 23 | 4-5 p.m. | 220 Jacobs Hall

LUNAR technical lead Sara Cinnamon will speak at Jacobs Hall, sharing perspectives from her time in grad school at MIT to running her own startup in consumer healthcare to joining a world-class design firm.

### Organization, Hydration, Ion Speciation, and Inherent Electric Fields at Water Surfaces

Seminar | January 23 | 4-5 p.m. | 120 Latimer Hall

College of Chemistry

We investigate ions and lipids at aqueous surfaces to better understand their complexation and speciation to then inform on atmospheric aerosol, cloud, and marine surface processes. The underlying driving forces for surface activity of bare aqueous surfaces with salts such as iron, magnesium, calcium and sodium chlorides are one class that is explored with aqueous surface selective experimental...   More >

### Thematic Seminar: Applied Mathematics: Nonlinear Fluid-Structure Interaction with Fiber-Reinforced Soft Composites: A Unified Mathematical Framework for Mathematical Analysis and Computation

Seminar | January 23 | 4:10-5 p.m. | 740 Evans Hall

Suncica Canic, University of Houston

Department of Mathematics

Fiber-reinforced structures arise in many engineering and biological applications. Examples include space inflatable habitats, vascular stents supporting compliant vascular walls, and aortic valve leaflets. In all these examples a metallic mesh, or a collection of fibers, is used to support an elastic structure, and the resulting composite structure has novel mechanical characteristics preferred...   More >

### Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Organizational Meeting

Seminar | January 23 | 5-6 p.m. | 939 Evans Hall

Ritvik Ramkumar, UC Berkeley

Department of Mathematics

The two topics for the student portion this semester are Intersection Theory and Linkage. A detailed outline of the topics for the first half of the seminar can be found at "math.berkeley.edu/~ritvik/Eisenbud-Seminar-Outline.pdf". In the meeting we will describe the main goals of this seminar and sign-up speakers for respective topics.

## Wednesday, January 24, 2018

### Understanding Secondary Organic Aerosol Thermodynamics, Mixing State and Phase with Models, Mimics, and Microfluidics

Seminar | January 24 | 11 a.m.-12 p.m. | 575 McCone Hall

Cari Dutcher, Assistant Professor, Department of Mechanical Engineering, University of Minnesota

College of Chemistry

Atmospheric aerosols are one of the major contributing factors to our climate, yet are a leading source of uncertainty in climate modeling. This uncertainty arises from the intricate nature of aerosol particles: these particles are complex microenvironments, which can contain multiple interfaces due to internal liquid – liquid phase partitioning and the external vapor – liquid surface. Aerosol...   More >

### MVZ LUNCH SEMINAR: Mohamed Noor "Recombination rate influences adaptation and speciation: Studies in the Drosophila pseudoobscura species group"

Seminar | January 24 | 12-1 p.m. | Valley Life Sciences Building, 3101 Grinnell-Miller Library

Mohamed Noor

Museum of Vertebrate Zoology

MVZ Lunch is a graduate level seminar series (IB264) based on current and recent vertebrate research. Professors, graduate students, staff, and visiting researchers present on current and past research projects. The seminar meets every Wednesday from 12- 1pm in the Grinnell-Miller Library. Enter through the MVZ's Main Office, 3101 Valley Life Sciences Building, and please let the receptionist...   More >

### Econ 235, Financial Economics: Job Market Seminar

Seminar | January 24 | 12-1:30 p.m. | C330 Haas School of Business

Yueran Ma, Harvard

Department of Economics

Joint with Haas Finance Seminar and Real Estate Seminar

### Plant and Microbial Biology Plant Seminar: "Regulation of vitamin 6 homeostasis "

Seminar | January 24 | 12-1 p.m. | 101 Barker Hall

Zack Zheng-Hui He

My lab is interested in utilizing a combination of cell, molecular, biochemical and genetic approaches to understand how cells communicate during plant growth and development.

### “Revealing the Dynamic Roles of Splicing and Translation in Gene Regulation”

Seminar | January 24 | 12-1 p.m. | 106 Stanley Hall

Liana Lareau, University of California, Berkeley

Bioengineering (BioE)

A single genome produces the huge diversity of cells and tissues needed to make a human by regulating gene expression to turn on and off the right genes at the right times. The final, post-transcriptional steps of gene expression — RNA processing and translation — are essential to the proper outcome. My goal is to understand what the cell achieves by adding extra layers of regulation at these...   More >

### Drivers of infectious disease dynamics: Quantifying the impact of demography and climate: Ayesha Mahmud PhD

Colloquium | January 24 | 12-1 p.m. | 2232 Piedmont, Seminar Room

Ayesha Mahmud PhD, Rockefeller Foundation Planetary Health Postdoctoral Fellow, Harvard University

A lunch time talk and discussion session, featuring visiting and local scholars presenting their research on a wide range of topics of interest to demography.

### Towards artificial general intelligence: Brain-inspired CAPTCHA breaking and Atari playing

Seminar | January 24 | 12-1 p.m. | 560 Evans Hall

Miguel Lázaro-Gredilla, Vicarious, Inc.

Abstract: Compositionality, generalization, and learning from a few examples are among the hallmarks of human intelligence. In this talk I will describe how Vicarious combines these ideas to create approaches to CAPTCHA breaking and Atari game playing that improve on the state of the art. Both of these tasks have indeed been tackled before, using respectively Convolutional Neural Networks (CNNs)...   More >

### Habits: The Good, The Bad, and The Ugly (BEUHS052)

Workshop | January 24 | 12:10-1:30 p.m. | Tang Center, University Health Services, Section Club

Beth Greivel, LMFT, Employee Assistance, Be well at Work - Employee Assistance

Habits form the structure of our lives. Habits matter because 40% of what we do every day is governed by them. What we eat, how much we move our bodies, how much we sleep, how we treat the people in our lives are all determined largely by habits. Healthy habits help us to be healthy and happy. Unhealthy habits keep us from living the lives we want.

In this workshop we will explore how habits...   More >

### Gender and Race Gatekeeping

Colloquium | January 24 | 12:10-1:15 p.m. | 5101 Tolman Hall

Michelle "Mikki" Hebl, Professor, Rice University

In this talk, Mikki will discuss the role of gatekeepers in preventing indviduals, often women and members of underrepresented groups, from attaining their potential. Mikki will review some of her programmatic research on subtle discrimination and will then provide some of her most recent studies and data on gender and race gatekeeping.

### Pronunciation Tips Workshop

Workshop | January 24 | 1-2 p.m. | International House, Auditorium

Take advantage of this opportunity to learn practical tools for improving your American-English pronunciation. This workshop will be taught by a professional ESL instructor from the English Studies Institute. Please register here: https://tinyurl.com/yakfjz8d

### Topology Seminar (Introductory Talk): An introduction to fibered 3-manifolds and the Thurston norm

Seminar | January 24 | 2-3 p.m. | 740 Evans Hall

Michael Landry, Yale University

Department of Mathematics

We will introduce Thurston's norm on the second homology of a 3-manifold, and some associated constructions including branched surfaces and Agol’s veering triangulation.

### Optically probing the neural basis of perception

Seminar | January 24 | 3:30-4:30 p.m. | 100 Genetics & Plant Biology Building

Hillel Adesnik, University of California, Berkeley, Molecular and Cell Biology

### ERG Colloquium: Diego Ponce De Leon Barido: Demand-side, User-centered, Sustainable Decarbonization in Resource Constrained Environments

Colloquium | January 24 | 4-5:30 p.m. | 126 Barrows Hall

Diego Ponce De Leon Barido, Recent ERG PhD Graduate, Energy and Resources Group

Energy and Resources Group

DESCRIPTION:
Future growth in urbanization will mainly occur in cities of the rising south. UN Habitat reports that in the past decade, the urban population in emerging economies grew on average 1.2 million people per week. By 2050, it is expected that seven out of ten people will be living in cities. Accompanying urbanization, information and communication technologies have also seen...   More >

### Applied Math Seminar: Using spacetime tents to solve hyperbolic systems

Seminar | January 24 | 4-5 p.m. | 736 Evans Hall

Jay Gopalakrishnan, Portland State University

Department of Mathematics

(Note the special location) A spacetime simulation region can be subdivided into tent-shaped subregions. Tents appear to be natural for solving hyperbolic equations. Indeed, one can ensure causality by constraining the height of the tent pole. More precisely, the domain of dependence of all points within the tent can be guaranteed to be contained within the tent, by constraining the tent pole...   More >

### Topology Seminar (Main Talk): Taut branched surfaces which span fibered faces

Seminar | January 24 | 4-5 p.m. | 3 Evans Hall

Michael Landry, Yale University

Department of Mathematics

Let $$M$$ be a closed hyperbolic 3-manifold with a fibered face $$\sigma$$ of the unit ball of the Thurston norm on $$H_2(M)$$. If $$M$$ satisfies a certain condition related to Agol’s veering triangulation, we can construct a taut branched surface in $$M$$ spanning $$\sigma$$. This partially answers a 1986 question of Oertel, and extends an earlier partial answer due to Mosher.

### EECS Colloquium: Meta Learning and Self Play

Colloquium | January 24 | 4-5 p.m. | Soda Hall, 306 (HP Auditorium)

Ilya Sutskever, OpenAI

In the first part, I will talk about meta learning, which is the problem of training a system that quickly learns to solve a wide variety of tasks. I will present several meta learning algorithms that can quickly solve simulated robotics tasks, and show how a simple meta learning approach can address the sim2real problem in robotics.

The second part will be on self play. Self play systems come...   More >

### Ice-nine and the Origins of Frank-Kasper and Quasicrystal Phases in Diblock Copolymer Melts

Colloquium | January 24 | 4-6 p.m. | 180 Tan Hall

Frank Bates, University of Minnesota

Block polymers have captured the interest of scientists and engineers for more than half a century. In general, the phase behavior of diblock copolymers, the simplest category of such self-assembling macromolecules, has been accepted as thoroughly understood. Recent experiments with low molecular weight diblock copolymers have revealed remarkable phase complexity in the limit of asymmetric...   More >

### Thematic Seminar: Partial Differential Equations: On the Strong Cosmic Censorship Conjecture in General Relativity

Seminar | January 24 | 4:10-5 p.m. | 740 Evans Hall

Sung-Jin Oh, Korea Institute for Advanced Study

Department of Mathematics

An intriguing feature of the explicit charged (Reissner-Nordstrom) or spinning (Kerr) black hole spacetimes is the existence of a regular Cauchy horizon, beyond which the Einstein equation loses its predictive power. The strong cosmic censorship conjecture of Penrose is a bold claim that, nevertheless, such a pathological behavior is nongeneric.

In this lecture, I will give a short introduction...   More >

### The Business of Disaster: Colonial and Neoliberal Governance in Post-Maria Puerto Rico

Panel Discussion | January 24 | 6:30-8:30 p.m. | 221 Kroeber Hall

Vincanne Adams, Professor, Joint UCSF/UC Berkeley Program in Medical Anthropology; Cathy Kennedy, Registered Nurse and Vice President, National Nurses United; Javier Arbona, Professor, American Studies and Design, UC Davis

Berkeley Center for Social Medicine, California Nurses Association/National Nurses United

The ongoing catastrophe following Hurricane Maria’s landfall on Puerto Rico in September reminds us that disasters are never merely natural. The enduring colonial relationship between the United States and Puerto Rico and the market-driven nature of governmental relief efforts are both critical to understanding the current crisis.

### Workshop: Introduction to Deep Learning

Workshop | January 24 | 8-10 p.m. | 306 Soda Hall

Machine Learning at Berkeley

Are you interested in learning what's the machinery behind the Deep Learning hype? Come to the ML@B Deep Learning Workshop! We will teach you how neural networks work and how to use them through hands on demos. The workshop is structured so that you have enough knowledge to get the most out of our future workshops. You can find the full list at ml.berkeley.edu/workshops. Although not strict...   More >


text:
### Functional Commitments for All Functions, with Transparent Setup and from SIS

##### Abstract

A *functional commitment* scheme enables a user to concisely commit to a function from a specified family, then later concisely and verifiably reveal values of the function at desired inputs. Useful special cases, which have seen applications across cryptography, include vector commitments and polynomial commitments. To date, functional commitments have been constructed (under falsifiable assumptions) only for functions that are essentially *linear*, with one recent exception that works for arbitrarily complex functions. However, that scheme operates in a strong and non-standard model, requiring an online, trusted authority to generate special keys for any opened function inputs. In this work, we give the first functional commitment scheme for nonlinear functions---indeed, for *all functions* of any bounded complexity---under a standard setup and a falsifiable assumption. Specifically, the setup is transparent,'' requiring only public randomness (and not any trusted entity), and the assumption is the hardness of the standard Short Integer Solution (SIS) lattice problem. Our construction also has other attractive features, including: *stateless updates* via generic composability; excellent *asymptotic efficiency* for the verifier, and also for the committer in important special cases like vector and polynomial commitments, via preprocessing; and *post-quantum security*, since it is based on SIS.

Note: Updated to discuss several concurrent related works and add zero-knowledge variant.

Available format(s)
Category
Public-key cryptography
Publication info
Keywords
functional commitmentsvector commitmentspolynomial commitmentsfully homomorphic computation
Contact author(s)
ldec @ mit edu
cpeikert @ umich edu
History
2023-02-28: revised
See all versions
Short URL
https://ia.cr/2022/1368

CC BY-NC-ND

BibTeX

@misc{cryptoeprint:2022/1368,
author = {Leo de Castro and Chris Peikert},
title = {Functional Commitments for All Functions, with Transparent Setup and from SIS},
howpublished = {Cryptology ePrint Archive, Paper 2022/1368},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/1368}},
url = {https://eprint.iacr.org/2022/1368}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.


text:
# The Unapologetic Mathematician

## Taylor’s Theorem

Like I said yesterday, because of extraneous terms the higher differentials don’t transform well, and so they’re not going to be useful for many of our purposes. However, there’s one thing it’s really good for: generalizing Taylor’s theorem. Specifically, the version of Taylor’s theorem that resembles the mean value theorem. And we’ll even use an approach like we did for the extension of that result to higher dimensions.

So let’s say that $f$ has continuous partial derivatives up to order $m$ in an open region $X\subseteq\mathbb{R}^n$. If $a$ and $b$ are two points in $X$ so that the whole line segment $(a,b)$ is contained in $X$, then there exists some point $\xi$ along that segment so that

$\displaystyle f(b)-f(a)=\sum\limits_{k=1}^{m-1}\frac{1}{k!}d^kf(a;b-a)+\frac{1}{m!}d^mf(\xi;b-a)$

Just like with the mean value theorem, we’ll define a new function $h(t)=f(a+t(b-a))$ for $t$ in the closed interval $[0,1]$. This is a composite of the function $f$ with the function $g(t)=a+t(b-a)$. This function is clearly differentiable, with constant derivative $g'(t)=b-a$. And so the chain rule tells us that

\displaystyle\begin{aligned}h'(t)&=dh(t)\\&=df(g(t))dg(t)\\&=df(g(t))(b-a)\\&=\left[D_if\right](t)(b^i-a^i)\\&=df(g(t);b-a)\end{aligned}

where we’ll fudge the distinction between the derivative and the differential of $h$ because it’s a real-valued function of a single real variable.

But now we can do the same thing to take the second derivative.

$\displaystyle h''(t)=\frac{d}{dt}\left[D_if\right](t)(b^i-a^i)=\left[D_{j,i}f\right](t)(b^j-a^j)(b^i-a^i)=d^2f(g(t);b-a)$

and so on, with each derivative of $h$ being given by a similar formula

$\displaystyle h^{(k)}(t)=d^kf(g(t);b-a)$

up until the index $k=m$. Beyond that we don’t know that the higher differentials exist.

Now we take all these derivatives and stick them into the usual one-variable Taylor theorem, which tells us that

$\displaystyle h(1)=h(0)+\sum\limits_{k=1}^{m-1}\frac{1}{k!}h^{(k)}(0)(1-0)^k+\frac{1}{m!}h^{(m)}(\tau)(1-0)^m$

for some $\tau$ in the interval $(0,1)$. With our formulæ for $h$ and its derivatives, this becomes

$\displaystyle f(b)-f(a)=\sum\limits_{k=1}^{m-1}\frac{1}{k!}d^kf(a;b-a)+\frac{1}{m!}d^mf(\xi;b-a)$

where $\xi=a+\tau(b-a)$ is a point on the line segment $(a,b)$, and the theorem is proved.

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October 20, 2009 - Posted by | Analysis, Calculus

## 2 Comments »

1. […] we have analytic functions. Once we’re in and we have all higher derivatives we can use Taylor’s theorem to write out the Taylor series of our function. But this may or may not converge back to the […]

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text:
org.apache.commons.math4.distribution

• ### Nested classes/interfaces inherited from interface org.apache.commons.math4.distribution.RealDistribution

RealDistribution.Sampler
• ### Field Summary

Fields
Modifier and Type Field and Description
static double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
Default inverse cumulative probability accuracy.
• ### Fields inherited from class org.apache.commons.math4.distribution.AbstractRealDistribution

SOLVER_DEFAULT_ABSOLUTE_ACCURACY
• ### Constructor Summary

Constructors
Constructor and Description
BetaDistribution(double alpha, double beta)
Creates a new instance.
BetaDistribution(double alpha, double beta, double inverseCumAccuracy)
Creates a new instance.
• ### Method Summary

All Methods
Modifier and Type Method and Description
RealDistribution.Sampler createSampler(org.apache.commons.rng.UniformRandomProvider rng)
Creates a sampler.
double cumulativeProbability(double x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
double density(double x)
Returns the probability density function (PDF) of this distribution evaluated at the specified point x.
double getAlpha()
Access the first shape parameter, alpha.
double getBeta()
Access the second shape parameter, beta.
double getNumericalMean()
Use this method to get the numerical value of the mean of this distribution.
double getNumericalVariance()
Use this method to get the numerical value of the variance of this distribution.
protected double getSolverAbsoluteAccuracy()
Return the absolute accuracy setting of the solver used to estimate inverse cumulative probabilities.
double getSupportLowerBound()
Access the lower bound of the support.
double getSupportUpperBound()
Access the upper bound of the support.
boolean isSupportConnected()
Use this method to get information about whether the support is connected, i.e.
double logDensity(double x)
Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x.
• ### Methods inherited from class org.apache.commons.math4.distribution.AbstractRealDistribution

inverseCumulativeProbability, probability, probability, sample
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Field Detail

• #### DEFAULT_INVERSE_ABSOLUTE_ACCURACY

public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
Default inverse cumulative probability accuracy.
Since:
2.1
Constant Field Values
• ### Constructor Detail

public BetaDistribution(double alpha,
double beta)
Creates a new instance.
Parameters:
alpha - First shape parameter (must be positive).
beta - Second shape parameter (must be positive).

public BetaDistribution(double alpha,
double beta,
double inverseCumAccuracy)
Creates a new instance.
Parameters:
alpha - First shape parameter (must be positive).
beta - Second shape parameter (must be positive).
inverseCumAccuracy - Maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
Since:
3.1
• ### Method Detail

• #### getAlpha

public double getAlpha()
Access the first shape parameter, alpha.
Returns:
the first shape parameter.
• #### getBeta

public double getBeta()
Access the second shape parameter, beta.
Returns:
the second shape parameter.
• #### density

public double density(double x)
Returns the probability density function (PDF) of this distribution evaluated at the specified point x. In general, the PDF is the derivative of the CDF. If the derivative does not exist at x, then an appropriate replacement should be returned, e.g. Double.POSITIVE_INFINITY, Double.NaN, or the limit inferior or limit superior of the difference quotient.
Parameters:
x - the point at which the PDF is evaluated
Returns:
the value of the probability density function at point x
• #### logDensity

public double logDensity(double x)
Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x. In general, the PDF is the derivative of the CDF. If the derivative does not exist at x, then an appropriate replacement should be returned, e.g. Double.POSITIVE_INFINITY, Double.NaN, or the limit inferior or limit superior of the difference quotient. Note that due to the floating point precision and under/overflow issues, this method will for some distributions be more precise and faster than computing the logarithm of RealDistribution.density(double).

The default implementation simply computes the logarithm of density(x).

Specified by:
logDensity in interface RealDistribution
Overrides:
logDensity in class AbstractRealDistribution
Parameters:
x - the point at which the PDF is evaluated
Returns:
the logarithm of the value of the probability density function at point x
• #### cumulativeProbability

public double cumulativeProbability(double x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x). In other words, this method represents the (cumulative) distribution function (CDF) for this distribution.
Parameters:
x - the point at which the CDF is evaluated
Returns:
the probability that a random variable with this distribution takes a value less than or equal to x
• #### getSolverAbsoluteAccuracy

protected double getSolverAbsoluteAccuracy()
Return the absolute accuracy setting of the solver used to estimate inverse cumulative probabilities.
Overrides:
getSolverAbsoluteAccuracy in class AbstractRealDistribution
Returns:
the solver absolute accuracy.
Since:
2.1
• #### getNumericalMean

public double getNumericalMean()
Use this method to get the numerical value of the mean of this distribution. For first shape parameter alpha and second shape parameter beta, the mean is alpha / (alpha + beta).
Returns:
the mean or Double.NaN if it is not defined
• #### getNumericalVariance

public double getNumericalVariance()
Use this method to get the numerical value of the variance of this distribution. For first shape parameter alpha and second shape parameter beta, the variance is (alpha * beta) / [(alpha + beta)^2 * (alpha + beta + 1)].
Returns:
the variance (possibly Double.POSITIVE_INFINITY as for certain cases in TDistribution) or Double.NaN if it is not defined
• #### getSupportLowerBound

public double getSupportLowerBound()
Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return

inf {x in R | P(X <= x) > 0}.

The lower bound of the support is always 0 no matter the parameters.
Returns:
lower bound of the support (always 0)
• #### getSupportUpperBound

public double getSupportUpperBound()
Access the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1). In other words, this method must return

inf {x in R | P(X <= x) = 1}.

The upper bound of the support is always 1 no matter the parameters.
Returns:
upper bound of the support (always 1)
• #### isSupportConnected

public boolean isSupportConnected()
Use this method to get information about whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support. The support of this distribution is connected.
Returns:
true
• #### createSampler

public RealDistribution.Sampler createSampler(org.apache.commons.rng.UniformRandomProvider rng)
Creates a sampler. Sampling is performed using Cheng's algorithm:
 R. C. H. Cheng,
"Generating beta variates with nonintegral shape parameters",
Communications of the ACM, 21, 317-322, 1978.

Specified by:
createSampler in interface RealDistribution
Overrides:
createSampler in class AbstractRealDistribution
Parameters:
rng - Generator of uniformly distributed numbers.
Returns:
a sampler that produces random numbers according this distribution.


text:
# Assignment 1

due at 23:59 on   +80

# Software setup

For the first part of this assignment, I’d like you to set up the tools for Haskell programming, both in the lab and on your own machine (laptop or desktop).

## Stack and GHC

“Stack” is a build tool and dependency manager for Haskell projects. “GHC” is the Glasgow Haskell Compiler, which Stack can download for you. They work on every popular platform (Windows, Mac, Linux).

Start by following installation instructions here: https://docs.haskellstack.org/en/stable/install_and_upgrade/

For Mac and Linux, that page recommends a curl command; you would run that in the Terminal application (in Applications » Utilities on the Finder menu). For Windows, there’s a traditional installation program.

Once installed, you will also use Stack from the Terminal application, called the Command Prompt on Windows. To launch the Windows Command Prompt, open the start menu and type cmd – you should see the Command Prompt application appear as the best match. Press enter to open it.

On either platform, verify that Stack is installed correctly by typing stack in the terminal, and pressing enter. You should see output similar to what follows:

stack - The Haskell Tool Stack

Usage: stack [--help] [--version] [--numeric-version]
[--hpack-numeric-version] [--docker*] [--nix*]
([--verbosity VERBOSITY] | [-v|--verbose] |
[--silent]) [--[no-]time-in-log]

[...lots more options...]

stack's documentation is available at https://docs.haskellstack.org/

stack setup

Once it is successfully installed, you should be able to type:

stack ghci

and be loaded into the interactive loop. It should look something like this:

Configuring GHCi with the following packages:
GHCi, version 8.0.2: http://www.haskell.org/ghc/  :? for help
Loaded GHCi configuration from C:\Users\Christopher League\AppData\Local\Temp\ghci5708\ghci-script
Prelude>

To quit GHCi, just type :q then enter.

## Editor

You will need to use a text editor, ideally one with at least some support for Haskell syntax highlighting. On Windows, a good choice is Notepad++ https://notepad-plus-plus.org/, but here are some others that work on multiple platforms:

If you experiment with anything else and like it, let us know!

## Hello, world!

Now we’ll try to compile and run a small “Hello world” program. This should probably be the first program you write with any new language or compiler. And although printing Hello is simple enough in Haskell, we won’t use console output (putStrLn) much more until we’re a few weeks into the course. (Remember, Haskell is a pure language, and console output is a side effect – so the way I/O works is a bit restrictive and unusual.)

Here’s how to start. Create a folder somewhere convenient (like Desktop or Documents) – I just called mine cs695. Don’t use spaces in your folder or file names – it makes them really inconvenient to specify from the command line.

Use your editor to type this program – I always suggest typing rather than copy and paste, because you learn the syntax better:

main = putStrLn "Hello world"

Save that text as a file called Hello.hs in your cs695 folder. Again, don’t use spaces in file names! Now in your Command Prompt or Terminal, you need to change to the folder where your code is saved:

cd Desktop/cs695

Once you’re there, the simplest way to compile and run your program is:

stack runghc Hello.hs

You should see your message appear on the console. Congratulations, your first Haskell program!

Now you may want to make a change and run it again. In class, I showed how to sequence together two different print statements, using the do keyword:

main = do
putStrLn "Hello grad students"
putStrLn "Bye again"

Try making a similar change and running the program again. Don’t forget to save the file in your editor after making changes!

# Functions

This section serves mainly as rough notes of some of the demonstrations I did in class on 7 September. It also contains instructions for testing your functions interactively.

Let’s first define some simple mathematical functions, such as:

$f(x) = x^2 + 3$

$g(x,y) = x - 2y$

There I’m using math notation, and here is a translation into Haskell:

f x = x*x + 3
g x y = x - 2*y

Notice that we do not use parentheses or commas to specify functions and arguments. The function f applied to x is simply written as f x.

## Interactive testing

To test these functions, we wouldn’t use stack runghc like we did with the “Hello world” program. They do not do any console output. Instead, we want to load their definitions into the interactive interpreter.

Save them into a .hs file (you can just add them to Hello.hs if you want), and then in your terminal, run:

stack ghci

At the Prelude> prompt, type :load Hello.hs. (Or you can just use :l as an abbreviation for :load.) Then you can interactively call the functions and inspect the results. Here’s a transcript where I did that:

C:\Users\Christopher League\Desktop\cs695>stack ghci
Configuring GHCi with the following packages:
GHCi, version 8.0.2: http://www.haskell.org/ghc/  :? for help
Loaded GHCi configuration from C:\Users\Christopher League\AppData\Local\Temp\ghci3240\ghci-script
[1 of 1] Compiling Main             ( Hello.hs, interpreted )
Ok, modules loaded: Main.
*Main> f 14
199
*Main> f 21
444
*Main> g 14 21
-28
*Main> g 15 (f 12)
-279
*Main> g (f 15) (f 12)
-66

Whenever you make changes to your program, you do not have to completely restart GHCi. Instead, just use the :reload command (abbreviated :r) and it will load the last thing again, and start using the new definitions. (As long as you saved it in your editor!)

## Conditions and guards

Some mathematical functions can be defined by specifying multiple cases, where a Boolean expression determines which definition to use. For example, here’s a mathematical specification of the function at the heart of the Collatz conjecture.

$c(n) = \left\{ \begin{array}{ll} n/2 & \mbox{if}\,n\,\mbox{even}\\ 3n+1 & \mbox{otherwise} \end{array}\right.$

We’ll look at a few ways to specify that in Haskell. First, we can use the if-then-else keywords:

collatz1 n =
if even n then n div 2
else 3*n + 1

The function even is built-in, so we don’t have to do a module operator like we would in C++/Java. Also note the division operator: we use div rather than / because we want to stick with integer division; / would produce floating-point answers.

The next variation uses two separate clauses or cases to specify the function, but adorns one of them with a guard – the part between the pipe | (which we read as “where”) and the equals =.

collatz2 n | even n = n div 2
collatz2 n = 3*n + 1

Finally, you can stick to one clause to define the function, but use two different guards. The catch-all one uses the keyword otherwise:

collatz3 n
| even n = n div 2
| otherwise = 3*n + 1

Try all of these in your GHCi, and ensure you get the expected answers for each one on several different parameters.

## Recursion

Recursive definitions are a staple of functional programming – much more common than in typical imperative languages. One of the ways to define the factorial function is recursive:

$n! = \left\{ \begin{array}{ll} 1 & \mbox{if}\,n\leq0\\ n \times (n-1)! & \mbox{otherwise} \end{array}\right.$

Here is a definition in Haskell, using two clauses and a guard:

fact n | n <= 0 = 1
fact n = n * fact (n-1)

In class, we tried this on numbers large and small. Haskell uses arbitrary-sized integers by default, so it can generate some impressive quantities pretty quickly:

*Main> fact 5
120
*Main> fact 10
3628800
*Main> fact 500
1220136825991110068701238785423046926253574342803192842192413588385
8453731538819976054964475022032818630136164771482035841633787220781
7720048078520515932928547790757193933060377296085908627042917454788
2424912726344305670173270769461062802310452644218878789465754777149
8634943677810376442740338273653974713864778784954384895955375379904
2324106127132698432774571554630997720278101456108118837370953101635
6324432987029563896628911658974769572087926928871281780070265174507
7684107196243903943225364226052349458501299185715012487069615681416
2535905669342381300885624924689156412677565448188650659384795177536
0894005745238940335798476363944905313062323749066445048824665075946
7358620746379251842004593696929810222639719525971909452178233317569
3458150855233282076282002340262690789834245171200620771464097945611
6127629145951237229913340169552363850942885592018727433795173014586
3575708283557801587354327688886801203998823847021514676054454076635
3598417443048012893831389688163948746965881750450692636533817505547
8128640000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000

# Exercises

So far, this document has contained setup instructions and notes on using Haskell. Starting in this section, you will do some exercises and turn in your answers. Save your Haskell code for this entire section as a01.hs and upload that file to this dropbox.

1. Rewrite the factorial function I defined above to use if-then-else instead of the pattern guard. Name it factIf. Test that it produces the expected results for some inputs like 5, 6, and 10.

2. Define this mathematical function using Haskell, name it quadratic, and test it (correct answers for some inputs are given below).

$q(a,b,c) = \frac{-b + \sqrt{b^2 - 4ac}}{2a}$

Note about negative numbers in Haskell: the syntax of the negative sign can be a little confusing; if you’re getting errors related to it, you should try surrounding the value with parentheses, such as (-9) rather than just -9. Also, the square-root function in Haskell is named sqrt, and it’s built-in (nothing to import).

*Main> quadratic 2 9 3
-0.36254139118231254
*Main> quadratic 1 (-1) (-1)
1.618033988749895
3. Define a function to calculate the volume of a sphere of a given radius. Name it sphere. Below are correct answers for some inputs. To represent $$\pi$$, you should use the built-in constant pi (lowercase).

*Main> sphere 1
4.1887902047863905
*Main> sphere 3.75
220.8932334555323
4. Here is a recursive function in Haskell:

slow x y
| x < y = x
| otherwise = slow (x-y) y

On paper, trace out the steps involved in evaluating slow 101 21, the same way we would for an algebraic expression. That is, determine the parameters x and y, check which case applies, then rewrite it. Repeat until the recursion completes and you get down to a single number.

Then you can transcribe your paperwork into Haskell comment near the function in a01.hs. Comments in Haskell are surrounded by {- and -} (similar to /* and */ in C++/Java) or single-line comments using -- (similar to // in C++/Java). For example, you can write:

{- My evaluation:
slow 101 21 ==
_______ ==
_______ ==
_______  (fill in the blanks)
-}
5. Read the introduction to the Collatz sequence on Wikipedia and/or watch this Numberphile video about Collatz.

Then write a recursive Haskell function collatzCount n that calculates the number of steps it takes to get from n down to 1. For example, the Wikipedia article states “the sequence for $$n=27$$, listed and graphed below, takes $$111$$ steps” so your function output in that case should be:

*Main> collatzCount 27
111

Your function can begin like this:

collatzCount n
| n <= 1 = 0   -- We're already at one, so zero steps
| otherwise =  __________ -- fill in the blank

and you should feel free to make use of the collatz1 (or similar) definitions given previously.

Here are a few other correct examples:

*Main> collatzCount 99
25
*Main> collatzCount 1024
10
*Main> collatzCount  118
33


text:
# zbMATH — the first resource for mathematics

Estimates in $$L^ p$$ for magnetic Schrödinger operators. (English) Zbl 0880.35034
Let $$H({\mathbf a},V)$$ be a magnetic Schrödinger operator $\sum_{j=1}^n\Biggl({1 \over i} {\partial \over \partial x_j } - a_j(x)\Biggr)^2 + V(x)$ in $${\mathbb{R}}^n, n \geq 3$$ and $$L_j = {1 \over i} {\partial \over \partial x_j } - a_j$$. Under certain conditions on $$\text{curl}{\mathbf a}$$ and $$V$$, given in terms of the reverse Hölder inequality (in particular, they are valid for polynomial coefficients), the estimates of the following type $\sum_{1\leq j,k \leq n}|L_jL_k f|\leq C_p|H({\mathbf a},V)f|, \qquad 1<p<\infty$ are proved. There are also similar weak-type (1,1) inequalities.

##### MSC:
 35J10 Schrödinger operator, Schrödinger equation 35B45 A priori estimates in context of PDEs 35Q40 PDEs in connection with quantum mechanics
##### Keywords:
weak-type inequalities; reverse Hölder inequality
Full Text:


text:
# How to test the statistical significance of AUC?

(Step 1) Using my predictive model, I predicted 1000 scores for my sample dataset.

(Step 2) I then calculate the random score using the same method for a randomized dataset. I firstly fit the distribution of the random score.

(Step 3) For each of my predictive score (1000 scores, in step 1), I calculated the p-values of getting a score larger than my predictive score for my sample sample dataset. Thus, 1000 p-values for my sample dataset are obtained.

(Step 4) As the real classification is known, by looking at the enrichment of true positive, I found when filter the sample dataset by p-values < 0.05. The best true positive values is obtained, which represents about 150 data from my sample dataset.

I then, want to test the predictive power of my model by doing AUC of the ROC (sensitivity vs 1- specificity plot).

However, I am facing a problem now, should I include all 1000 data for ROC plot to get the AUC, or should I only include those 150 data (p < 0.05) for my AUC analysis?

When I said p < 0.05, the p-value to obtain a score higher than my predictive score by random. In general speaking, does it means that 50% of my data are obtained by chance?

## Edit

Thanks for the comments from @AlefSin, @steffen and @Frank Harrell.

For easier to discuss, I have prepare a sample dataset (x) as follows:

• My model predicted score (assume it is normal distributed with mean=1, sd=1)
• random set (assume also has mean=1, sd=1)
• Probability for each predicted score
• class prediction are listed as below, as listed in four columns

x <- data.frame (predict_score=c(rnorm(50,m=1, sd=1)))
x$random <- rnorm(50, m=1, sd=1) x$probability <- pnorm(x$predict_score, m=mean(x$random),sd=sd(x$random)) x$class <- c(1,1,1,1,2,1,2,1,2,2,1,1,1,1,2,1,2,1,2,2,1,1,1,1,2,1,2,1,2,2,1,1,2,1,2,1,2,2,1,1,1,1,1,1,2,2,2,2,1,1)

I then did AUC for all data as follows for all data points:

library(caTools)
colAUC(x$predict_score, x$class, plotROC=T, alg=c("Wilcoxon","ROC"))

result:

       [,1]
1 vs. 2  0.6

Let's said if the enrichment of true positive is higher (Your runs may be differnt from mine, as rnorm give different results everytime) when I filter the dataset by p < 0.5, I did the AUC for a subset of the data as folows:

b <- subset(x, x$probability < 0.5) colAUC(b$predict_score, b\$class, plotROC=T, alg=c("Wilcoxon","ROC"))

result:

             [,1]
1 vs. 2 0.7401961

My question is: When I do AUC analysis, is it a must to do the analysis with the whole dataset, or should we do filter the dataset first based on enrichment of true positive or what ever criteria before doing AUC?

• Try this: E.R. DeLong, D.M. DeLong, and D.L. Clarke-Pearson (1988), "Comparing the Areas Under Two or More Correlated Receiver Operating Characteristic Curves: A Nonparametric Approach," Biometrics, 44, 837-845. It explains how ROC curve and the U-statistics are related, how to calculate the significance of AUC and also how to say if difference between two AUCs is statistically significant. – AlefSin Jul 8 '11 at 8:06
• @AlefSin why don't you make an answer ;) ? @anyone: Can someone verify that the procedure performed by the OP is correct ? @evdstat: (+1) a really interesting question – steffen Jul 8 '11 at 8:24
• @AlefSin, @steffen, Yes, please kindly comments if I have done it correctly or not. Many thanks again for your help. – evdstat Jul 8 '11 at 9:52
• It would be better to state your ultimate goals and to describe the candidate features (predictors) and their dimensionality, and also what is the dependent variable in its rawest form (e.g., before any dichotomization). Then we can better help you. – Frank Harrell Jul 8 '11 at 12:35
• @evdstat I merged your second post as an edit to this because it wasn't a new question and relied heavily on this one. – whuber Jul 8 '11 at 15:19


text:
Thesis Open Access

# Evolution of Planetary Nebulae with WR-type Central Stars

Danehkar, Ashkbiz

### DCAT Export

<?xml version='1.0' encoding='utf-8'?>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:adms="http://www.w3.org/ns/adms#" xmlns:cnt="http://www.w3.org/2011/content#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dct="http://purl.org/dc/terms/" xmlns:dctype="http://purl.org/dc/dcmitype/" xmlns:dcat="http://www.w3.org/ns/dcat#" xmlns:duv="http://www.w3.org/ns/duv#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:frapo="http://purl.org/cerif/frapo/" xmlns:geo="http://www.w3.org/2003/01/geo/wgs84_pos#" xmlns:gsp="http://www.opengis.net/ont/geosparql#" xmlns:locn="http://www.w3.org/ns/locn#" xmlns:org="http://www.w3.org/ns/org#" xmlns:owl="http://www.w3.org/2002/07/owl#" xmlns:prov="http://www.w3.org/ns/prov#" xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#" xmlns:schema="http://schema.org/" xmlns:skos="http://www.w3.org/2004/02/skos/core#" xmlns:vcard="http://www.w3.org/2006/vcard/ns#" xmlns:wdrs="http://www.w3.org/2007/05/powder-s#">
<rdf:type rdf:resource="http://www.w3.org/ns/dcat#Dataset"/>
<dct:type rdf:resource="http://purl.org/dc/dcmitype/Text"/>
<dct:identifier rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://doi.org/10.5281/zenodo.47794</dct:identifier>
<foaf:page rdf:resource="https://doi.org/10.5281/zenodo.47794"/>
<dct:creator>
<rdf:type rdf:resource="http://xmlns.com/foaf/0.1/Agent"/>
<foaf:name>Danehkar, Ashkbiz</foaf:name>
<foaf:givenName>Ashkbiz</foaf:givenName>
<foaf:familyName>Danehkar</foaf:familyName>
<org:memberOf>
<foaf:Organization>
<foaf:name>Macquarie University</foaf:name>
</foaf:Organization>
</org:memberOf>
</rdf:Description>
</dct:creator>
<dct:title>Evolution of Planetary Nebulae with WR-type Central Stars</dct:title>
<dct:publisher>
<foaf:Agent>
<foaf:name>Zenodo</foaf:name>
</foaf:Agent>
</dct:publisher>
<dct:issued rdf:datatype="http://www.w3.org/2001/XMLSchema#gYear">2014</dct:issued>
<dcat:keyword>Astronomy</dcat:keyword>
<dcat:keyword>Physics</dcat:keyword>
<dcat:keyword>Astrophysics</dcat:keyword>
<dcat:keyword>Planetary Nebulae</dcat:keyword>
<dcat:keyword>Wolf-Rayet Stars</dcat:keyword>
<dcat:keyword>Interstellar Medium</dcat:keyword>
<dcat:keyword>Stellar Evolution</dcat:keyword>
<dcat:keyword>Imaging Spectroscopy</dcat:keyword>
<dct:issued rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2014-04-24</dct:issued>
<skos:notation rdf:datatype="http://www.w3.org/2001/XMLSchema#string">2014PhDT........76D</skos:notation>
<owl:sameAs rdf:resource="https://hdl.handle.net/1959.14/337736"/>
<skos:notation rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://hdl.handle.net/1959.14/337736</skos:notation>
<skos:notation rdf:datatype="http://www.w3.org/2001/XMLSchema#string">urn:isbn:978-1-339-29933-4</skos:notation>
<owl:sameAs rdf:resource="https://zenodo.org/record/47794"/>
<skos:notation rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://zenodo.org/record/47794</skos:notation>
<dct:isVersionOf rdf:resource="https://doi.org/10.5281/zenodo.631175"/>
<dct:isPartOf rdf:resource="https://zenodo.org/communities/astrothesis"/>
<dct:description>
This thesis presents a study of the kinematics, physical conditions and chemical abundances for a sample of Galactic planetary nebulae (PNe) with Wolf-Rayet (WR) and weak emission-line stars (wels), based on optical integral field unit (IFU) spectroscopy obtained with the Wide Field Spectrograph (WiFeS) on the Australian National University 2.3 telescope at Siding Spring Observatory, and complemented by spectra from the literature. PNe surrounding WR-type stars constitute a particular study class for this study. A considerable fraction of currently well-identified central stars of PNe exhibit hydrogen-deficient&#39; fast expanding atmospheres characterized by a large mass-loss rate. Most of them were classified as the carbon-sequence and a few of them as the nitrogen-sequence of the WR-type stars. What are less clear are the physical mechanisms and evolutionary paths that remove the hydrogen-rich outer layer from these degenerate cores, and transform it into a fast stellar wind. The aim of this thesis is to determine kinematic structure, density distribution, thermal structure and elemental abundances for a sample of PNe with different hydrogen-deficient central stars, which might provide clues about the origin and formation of their hydrogen-deficient stellar atmospheres.

H&alpha; and [N II] emission features have been used to determine kinematic structures. Based on spatially resolved observations of these emission lines, combined with archival&nbsp;Hubble Space Telescope&nbsp;imaging for compact PNe, morphological structures of these PNe have been determined. Comparing the velocity maps from the IFU spectrograph with those provided by morpho-kinematic models allowed disentangling of the different morphological components of most PNe, apart from the compact objects. The results indicate that these PNe have axisymmetric morphologies, either bipolar or elliptical. In many cases, the associated kinematic maps for PNe around hot WR-type stars also show the presence of so-called fast low-ionization emission regions (FLIERs).

The WiFeS observations, complemented with archival spectra from the literature, have been used to carry out plasma diagnostics and abundance analysis using both collisionally excited lines (CELs) and optical recombination lines (ORLs). ORL abundances for carbon, nitrogen and oxygen have been derived where adequate recombination lines were available. The weak physical dependence of ORLs has also been used to determine the physical properties. It is found that the ORL abundances are several times higher than the CEL abundances, whereas the temperatures derived from the He I recombination lines are typically lower than those measured from the collisionally excited nebular-to-auroral forbidden line ratios. The abundance discrepancy factors (ADFs) for doubly-ionized nitrogen and oxygen are within a range from 2 to 49, which are closely correlated with the dichotomy between temperatures derived from forbidden lines and those from He I recombination lines. The results show that the ADF and temperature dichotomy are correlated with the intrinsic nebular H&beta;&nbsp;surface brightness, suggesting that the abundance discrepancy problem must be related to the nebular evolution.

Three-dimensional photoionization models of a carefully selected sample of Galactic PNe have been constructed, constrained by the WiFeS observations (Abell 48 and SuWt 2) and the double echelle MIKE spectroscopy from the literature (Hb 4 and PB 8). The WiFeS observations have been used to perform the empirical analysis of Abell 48 and SuWt 2. The spatially resolved velocity distributions were used to determine the kinematic structures of Hb 4 and Abell 48. The previously identified non-LTE model atmospheres of Abell 48 and PB 8 have been used as ionizing fluxes in their photoionization models. It is found that the enhancement of the [N II] emission in the FLIERs of Hb 4 is more attributed to the geometry and density distribution, while the ionization correction factor method and electron temperature used for the empirical analysis are mostly responsible for apparent inhomogeneity of nitrogen abundance. However, the results indicate that the chemically inhomogeneous models, containing a small fraction of metal-rich inclusions (around 5 percent), provide acceptable matches to the observed ORLs in Hb 4 and PB 8. The observed nebular spectrum of Abell 48 was best produced by using a nitrogen-sequence non-LTE model atmosphere of a low-mass progenitor star rather than a massive Pop I star. For Abell 48, the helium temperature predicted by the photoionization model is higher than those empirically derived, suggesting the presence of a fraction of cold metal-rich structures inside the nebula. It is found that a dual-dust chemistry with different grain species and discrete grain sizes likely produces the nebular&nbsp;Spitzer&nbsp;mid-infrared continuum of PB 8. The photoionization models of SuWt 2 suggest the presence of a hot hydrogen-deficient degenerate core, compatible with what is known as a PG 1159-type star, while the nebula&#39;s age is consistent with a born-again scenario.
</dct:description>
<dct:accessRights rdf:resource="http://publications.europa.eu/resource/authority/access-right/PUBLIC"/>
<dct:accessRights>
<rdfs:label>Open Access</rdfs:label>
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</dct:accessRights>
<dcat:distribution>
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<dcat:accessURL rdf:resource="https://doi.org/10.5281/zenodo.47794"/>
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</dcat:distribution>
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