# Ppt on polynomials of 99

##### What Crypto Can Do for You: Solutions in Search of Problems Anna Lysyanskaya Brown University.

E(c 1 )E(c 0 ) …using an “additive” encryption scheme E(x) * E(y) = E(x+y) [Paillier’99] Step 2: Alice encrypts her polynomial… Alice’s encrypted polynomial p(x) E(c 4 )E(c 3 )E(c 2 )E(c 1 )E(c 0 ) …using an “additive” encryption/ Solution for Two Parties: Yao’s Encrypted Circuit Alice’s logical circuit C Bob’s input x 0 1 1 Encrypted circuit Oblivious transfer of keys A More General Solution for N Parties: Secure Multi-Party Computation Split the computation into logical steps (ANDs, ORs, NOTs) or algebraic/

##### How NP got a new definition: Probabilistically Checkable Proofs (PCPs) & Approximation Properties of NP-hard problems SANJEEV ARORA PRINCETON UNIVERSITY.

Szegedy] 1992 MAX-3SAT Desired Way to disguise instances of any NP problem as instances of MAX-3SAT s.t. “Yes” instances turn into satisfiable formulae “No” instances turn into formulae in which < 0.99 fraction of clauses can be simultaneously satisfied “Gap” Cook-Levin/ MIP = NEXPTIME [Babai, Fortnow, Lund ’90] 1 st “PCP Theorem” Dinur [05]’s proof uses random walks on expander graphs instead of polynomials. Håstad’s 3-bit Theorem (and “fourier method”) NP = PCP(lg n, 1) T1T1 T2T2 c bits 1 bit YES instances/

##### Techniques for Computing and Using Bounds for Combinatorial Optimization Problems Sharlee Climer and Weixiong Zhang Department of Computer Science and.

of tour found Could derive a lower bound by rounding values down and keeping these values when computing cost of tour found IJCAI-05 TutorialBounding Techniques76 Modifying objective function coefficients Frieze’s polynomial-time STSP algorithm [SIAM Computing 1987] Frieze’s polynomial/range equal to number of cities Random ATSP graphs with cost range equal to number of cities Found close to half of the backbone arcs and 99% of the fat arcs Found close to half of the backbone arcs and 99% of the fat arcs /

##### Computing the Rational Univariate Reduction by Sparse Resultants Koji Ouchi, John Keyser, J. Maurice Rojas Department of Computer Science, Mathematics.

˜ ( n R A S A  ) or O ˜ ( S A 1+  ) if char K = 0 Texas A&M University ACA2004 14 RUR Complexity Analysis n [Rojas 99] l Evaluating Pert ( u ) requires O ˜ ( n R A 2 S A  ) or O ˜ ( S A 1+  ) if char K = 0 Texas A&M/ Texas A&M University ACA2004 29 RUR Future Work n RUR l Faster sparse resultant algorithms l Take advantages of sparseness of matrices [Emiris and Pan 97] l Faster univariate polynomial operations Texas A&M University ACA2004 30 RUR Thank you for listening! n Contact l Koji Ouchi, kouchi@/

##### A different view of independent sets in bipartite graphs Qi Ge Daniel Štefankovič University of Rochester.

, Jerrum ’02). Glauber dynamics does not mix in polynomial time for 6-regular bipartite graphs (example: union of 6 random matchings) (Dyer, Frieze, Jerrum ’02).  = maximum degree of G counting/sampling independent sets in bipartite graphs: A different view of independent sets in bipartite graphs polynomial time sampler for  5 (Dyer,Greenhill ’00, Luby,Vigoda’99, Weitz’06). no polynomial time sampler (unless NP=RP) for  25/

##### 7/2/2015Errors1 Transmission errors are a way of life. In the digital world an error means that a bit value is flipped. An error can be isolated to a single.

double errors –all errors of an odd length –all bursts of 16-bits or less, 99.997% of 17-bits, and 99.998% of 18-bits and longer. 7/2/2015Errors27 The Algorithm To compute the checksum –Append n 0s to the end of the message, where n is the number of bits in the checksum –The resulting value is divided by the generator polynomial –Each division step is/

##### Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 3.5 Multiplying Polynomials.

polynomials Multiply each term of the first polynomial by each term of the second polynomial, and then combine like terms. Multiplying Polynomials Martin-Gay, Prealgebra & Introductory Algebra, 3ed 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Multiply each of/25x 2 – 10xz – 10xz + 4z 2 = 25x 2 – 20xz + 4z 2 Multiplying Polynomials Example Martin-Gay, Prealgebra & Introductory Algebra, 3ed 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Multiply (2x 2 + x –/

##### Systematic Bounding Techniques for Combinatorial Optimization Sharlee Climer and Weixiong Zhang Department of Computer Science and Engineering Washington.

of tour found Could derive a lower bound by rounding values down and keeping these values when computing cost of tour found AAAI-05 TutorialBounding Techniques75 Modifying objective function coefficients Frieze’s polynomial-time STSP algorithm [SIAM Computing 1987] Frieze’s polynomial/range equal to number of cities Random ATSP graphs with cost range equal to number of cities Found close to half of the backbone arcs and 99% of the fat arcs Found close to half of the backbone arcs and 99% of the fat arcs Time/

##### Unit 19: Polynomial Regression. Learning Objectives  What is polynomial regression and when is it appropriate  Contrast with other non-linear methods.

(quadratic, cubic) are implicated by the distribution of residuals. How to Determine Order 12 Polynomial vs. Power Transformation of X Power Transformations of X Polynomial Regression 13 How does number of electives taken in an area predict interest in /paragraph optional in some cases] The overall effect of Number of Electives was significant, F(2,97) = 99.62, p<.0001, with Number of Electives accounting for 67.3% of the total variance in Interest. The linear effect of Electives was significant, B= 1.2, /

##### Of 31 09/19/2011UIUC: Communication & Computation1 Communication & Computation A need for a new unifying theory Madhu Sudan Microsoft, New England.

Algorithm Idea: Find algebraic explanation Find algebraic explanation of all points. of all points. Stare at it! Stare at it! Factor the polynomial! of 31 09/19/2011UIUC: Communication & Computation15 Decoding Algorithm Fact: There is always a degree 2n polynomial thru n points Fact: There is always a degree 2n polynomial thru n points Can be found in polynomial time (solving linear system). Can be found in/

##### The Complexity of the Network Design Problem Networks, 1978 Classic Paper Reading 99.12.

The Complexity of the Network Design Problem Networks, 1978 Classic Paper Reading 99.12 Outline Introduction NDP is NP-complete SNDP is NP-complete Conclusion 2 Introduction B96902094 傅莉雯 Combinatorial optimization is/3,4,5},{1,2,6}} No! Yes! Reduction Given any instance of EXACT 3-COVER, we define an instance of SNDP as follows: 31 = r Illustration of reduction 32 S T Illustration of reduction 33 R Illustration of reduction 34 S T R polynomial-time reduction Claim  has a feasible solution  if and only if/

##### Collaborative Data Sharing with Mappings and Provenance Todd J. Green University of Pennsylvania Spring 2009.

RCHESTRA, one kind of annotation (provenance polynomials) can support many kinds of trust models, ranking,... – Compute propagation of annotations just once Extends to recursive mappings Analysis of previous provenance models: – All special cases of framework – None/equivalence with where-provenance [Tan 03] Answering queries using views [Levy+ 95], [Chaudhuri+ 95], [Cohen+ 99], [Afrati+ 99],... View adaptation [Gupta+ 95], mapping adaptation [Velegrakis+ 03] 48 We studied an important practical problem – /

##### Curves and Surfaces in OpenGL Ed Angel Professor of Computer Science, Electrical and Computer Engineering, and Media Arts University of New Mexico.

and GLUT contain polynomial approximations of quadrics 4 Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005 One-Dimensional Evaluators Evaluate a Bernstein polynomial of any degree at a set of specified values Can evaluate a variety of variables ­Points along/ } must draw in both directions 13 Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005 Rendering with Quadrilaterals for(j=0; j<99; j++) { glBegin(GL_QUAD_STRIP); for(i=0; i<100; i++) { glEvalCoord2f ((float) i/100.0, (float) j/100./

##### CHAPTER 5: Public-key cryptography I. RSA

, a function F:N -> N is said to be one-way function if it is easily computable - in polynomial time - but any computation of its inverse is infeasible. A one-way permutation is a 1-1 one-way function. easy x f(x) /is that decoding seems to be infeasible. Example If A = (74, 82,94, 83, 39, 99, 56, 49, 73, 99) and B = (1100110101) then ABT = Public-key cryptography Design of knapsack cryptosystems IV054 Design of knapsack cryptosystems 1. Choose a superincreasing vector X = (x1,…,xn). 2. Choose m, u such/

##### Table of Contents Polynomials: The Remainder and Factor Theorems The remainder theorem states that if a polynomial, P(x), is divided by x – c, then the.

(1) = 2(1) 3 – (1) 2 + 3(1) – 4= 0. Since P(1) = 0, x – 1 is a factor. Table of Contents Polynomials: The Remainder and Factor Theorems Slide 3 Try:For the polynomial, P(x) = x 3 – x 2 + x – 6, (a) find P(5) using the remainder theorem, (b)use the factor theorem to show /that x – 2 is a factor. (a) 1- 1 1- 6 5 20 105 5 | 1 4 21 99 = P(5) (b)P(2) = (2) 3 – (2) 2 + (2) – 6 = 0 Since P(2) = 0, x – 2 is a factor. Table of Contents Polynomials: The Remainder and Factor Theorems

##### Principles of Econometrics, 4t h EditionPage 1 Chapter 4: Prediction, Goodness-of-fit, and Modeling Issues Chapter 4 Prediction, Goodness-of-fit, and Modeling.

the Regression Errors Normally Distributed? Principles of Econometrics, 4t h EditionPage 75 Chapter 4: Prediction, Goodness-of-fit, and Modeling Issues 4.4 Polynomial Models Principles of Econometrics, 4t h EditionPage 76 Chapter 4: Prediction, Goodness-of-fit, and Modeling Issues In addition / is: 4.5.4 A Generalized R 2 Measure 4.5 Log-linear Models Principles of Econometrics, 4t h EditionPage 99 Chapter 4: Prediction, Goodness-of-fit, and Modeling Issues For the wage equation, the general R 2 is: – /

##### 1 Erice 2005, the Analysis of Patterns. Grammatical Inference 1 Colin de la Higuera Grammatical inference: techniques and algorithms.

99 Erice 2005, the Analysis of Patterns. Grammatical Inference 99 Definitions Let  be the length-lex ordering over  * Let Pref(L) be the set of all prefixes of strings in some language L. 10 0 Erice 2005, the Analysis of / Erice 2005, the Analysis of Patterns. Grammatical Inference 126 Properties (4) Polynomial aspects Polynomial characteristic sets Polynomial update time But not necessarily a polynomial number of mind changes 12 7 Erice 2005, the Analysis of Patterns. Grammatical Inference 127 Extensions/

##### Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 12 Exponents and Polynomials.

Pearson Education, Inc. Publishing as Prentice Hall. To Multiply Two Polynomials Multiply each term of the first polynomial by each term of the second polynomial, and then combine like terms. Multiplying Polynomials Martin-Gay, Developmental Mathematics, 2e 55 Copyright © 2011 Pearson / – 2z) = 25x 2 – 10xz – 10xz + 4z 2 = 25x 2 – 20xz + 4z 2 Example Martin-Gay, Developmental Mathematics, 2e 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Multiply (2x 2 + x – 1)(x 2 + 3x + 4). (2x 2/

##### Week 2 of MTH 209. Due for this week…  Homework 2 (on MyMathLab – via the Materials Link)  Monday night at 6pm.  Read Chapter 6.6-6.7, 7.6-7.7, 10.5,

2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Rational expressions can be written as quotients (fractions) of two polynomials. Examples include: Basic Concepts Slide 45 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE/radical expressions Q 77-88  Rationalizing the denominator Q 89-98  Using a conjugate to rationalize the denominator Q 99-102  Rationalizing the denominator Q 103-108  Rationalizing the denominator having a cube root Q 113-116 Slide /

##### Data Abstraction Gang Qian Department of Computer Science University of Central Oklahoma.

array containing zero The latter is used in the implementation  For convenience, an instance variable is used to store the degree of the Poly /** OVERVIEW: Polys are immutable polynomials with integer coefficients. A typical Poly is c0 + c1x + c2x^2 +... */ public class Poly { private int[] trms/above rep, if an integer i between 0 and 99 is in the set, we just set els[i] to be true  All integers > 99 are stored in otherEls  For efficiency purpose, we store the size of the set in sz  This will be an /

##### Zhihong Ye University of Virginia E08014 Collaboration, Hall-A, JLab Spokespersons: John Arrington, Donal Day, Doug Higinbotham, Patricia Solvignon Study.

of data with the same seeds: 1, New Forward + Old Backward  Simulate the REAL DeltaP reconstruction on HRS-R (δp wrong ); 2, New Forward + New Backward  Simulate the CORRECTED DeltaP reconstruction (δp right ). but wrong! E08-014 Data Analysis -DeltaP  HRS Optics  Polynomials/ Cross Sections  Cuts & Efficiencies  VDC One-Track-Only Cuts (> 99%);  Trigger Cuts (>99% since GC included);  PID Cuts (very loose cuts, 99% for GC, 99% for Calo);  Focal Plane Variables Cuts (removing big-angle events); /

##### Precalculus Chapter 2 Polynomial and Rational Functions.

by Factoring Step 1: Write the equation in standard form, ax 2 + bx + c = 0. Step 2: Factor the polynomial on the left side of the equation. Step 3: Set each factor found in Step 2 equal to zero using the Zero-Product Property Step 4: Solve /Write a formula s(t) that models the height of the baseball after t seconds. b) How high is the baseball after 2 seconds? c) Find the maximum height of the baseball. Support your answer graphically. Solution a) b) Baseball is 99 feet high after 2 seconds. c) Because a is/

##### Copyright ©2006 Brooks/Cole A division of Thomson Learning, Inc. Introduction to Probability and Statistics Twelfth Edition Robert J. Beaver Barbara M.

models, use R 2 (adj) to compare their effectiveness. 5.Use diagnostic plots to check for violation of the regression assumptions. Copyright ©2006 Brooks/Cole A division of Thomson Learning, Inc. A Polynomial Model quadraticWhen k = 2, the model is quadratic: A response y is related to a single independent /0.000 x2 866.7 305.3 2.84 0.022 x1x2 260.13 87.06 2.99 0.017 S = 201.344 R-Sq = 99.2% R-Sq(adj) = 98.9% Analysis of Variance Source DF SS MS F P Regression 3 42108777 14036259 346.24 0.000 Residual /

##### POLYNOMIAL TIME HEURISTIC OPTIMIZATION METHODS APPLIED TO PROBLEMS IN COMPUTATIONAL FINANCE Ph.D. dissertation of Fogarasi Norbert, M.Sc. Supervisor: Dr.

one that yields the largest max eigenvalue. Amounts to solving (n − k) generalized eigenvalue problems of size k + 1. Polynomial runtime: 17 Polynomial Time Heuristic Approaches Truncation Method (Fogarasi et al 2012) Compute unconstrained solution then use k heaviest dimensions/, EDD – Earliest Due Date) Job size 510152030405075100 % outperf 99.9100 99.599.299.699.398.698.8 38 Thesis II.3 Further improving HNN Smart HNN (SHNN) Use the result of Largest Weighted Path First (LWPF) as starting point for HNN /

##### Oct 18, MIT1 Survey and Recent Results: Robust Geometric Computation Chee Yap Department of Computer Science Courant Institute New York University.

MIT32 Root Bound A root bound for an expression E is a value such that n E.g., the Cauchy’s bound says that because is a root of the polynomial x 4  0 x 2  1. n Root bit-bound is defined as  log(b) b > 0  b  =  Oct 18/ routinely construct robust programs * n Current Libraries:  Real/Expr [Yap-Dube’94]  LEDA real [Burnikel et al’99]  Core Library [Karamcheti et al’99] Oct 18, 2001Talk @ MIT37 Core Library n An EGC Library y C++, compact (200 KB) y Focus on “Numerical Core/

##### Rafael Pass Cornell University Limits of Provable Security From Standard Assumptions.

Let (C,t) be a k(.)-round intractability assumption where k is a polynomial. If there exists a PPT reduction R for basing security of any of previously mentioned schemes, on the hardness of (C,t), then there exists a PPT attacker B that breaks (C,t/can find (recursively) find one proof where nesting depth is “small” Use Techniques reminiscent of Concurrent ZK a la [RK’99], [CPS’10] x2x2 x3x3 rewinding here: redo work of nested sessions w2w2 w3w3 w1w1 General Reductions: Problem II Problem: R might not only /

##### 1 Robust PCPs of Proximity (Shorter PCPs, applications to Coding) Eli Ben-Sasson (Radcliffe) Oded Goldreich (Weizmann & Radcliffe) Prahladh Harsha (MIT)

- special case of “PCP Spot Checkers” PCPPs - special case of “PCP Spot Checkers” [EKR ’99] [EKR ’99] PCPP – extension of Property Testing PCPP – extension of Property Testing [RS ’92, GGR ’96] [RS ’92, GGR ’96] Assignment Testers of [DR ’03] similar to PCPPs. Assignment Testers of [DR ’03]/f ) < d and l – line, then f restricted to line l is a univariate polynomial of degree < d. If deg( f ) < d and l – line, then f restricted to line l is a univariate polynomial of degree < d. P r [ f ( x ) = g ( x )] · /

##### Information Theoretic Approach to Minimization of Logic Expressions, Trees, Decision Diagrams and Circuits.

2/16) log 2 (2/8) - (6/16) log 2 (6/8) = 0.88 bit Mutual Information I(f;x 1 )= 0.99 - 0.88 = 0.11 bit Information theoretical measures x 1 x 2 x 3 x 4 0 0 1 1 0 1 0 0 1 1 /will be applied to Galois Logic Shannon entropy Information theoretic criterion in minimization of polynomial expressions in GF(4) Linearly Independent Expansions in any Logic New Idea Shannon entropy Information theoretic criterion in minimization of trees, lattices and flattened forms in this logic Shannon decomposition Shannon entropy /

##### Optimization, Learnability, and Games: From the Lens of Smoothed Analysis Shang-Hua Teng Computer School of TexPoint fonts.

Nearly Tight Smoothed Bounds for 2D: Many Moments Three or More Objectives Not So Tight Yet: But Polynomial Smoothed Bound for Fixed Dimensions This Talk Part I: Overview of Smoothed Analysis Part II : Multi-objective Optimization Part III: Machine Learning Part VI: Games, Markets / LEGIT x4x4 YES NO YESSPAM x5x5 YES NOYES SPAM [Valiant84] P.A.C Learning Poly-time learning algorithm –Succeed with prob. ≥ 1-  (e.g. 0.99) –m = # examples = poly(n/ε) Output: h: X → {–1,+1} with err(h) = Pr x←D [ h(x)≠f(x) ] /

##### Lecture 5 Advanced (= Modern) Regression Analysis NUMERICAL ANALYSIS OF BIOLOGICAL AND ENVIRONMENTAL DATA John Birks.

of a joint) and continuous second derivatives (the rate of change in the slope of the line will not change across a joint). A spline of degree n will have continuous derivatives across the points up to order n – 1. R Mathematical Explanation A smoothly joined piecewise polynomial of/trees (b, e, h), each of which accounted for > 99% of the total ss. COMPARISON OF CART AND GLMs ANOVA is powerful technique but as number of predictor variables and complexity of data increase (interactions, unbalanced designs, /

##### Numerical Analysis of Processes NAP2 Physical models (transport equations, energy and entropy principles). Empirical models (neural networks and regression.

hours (samples were weighed at 15 minute intervals), the total available 154 values of specific humidity of grain for various temperatures and times. From these values only the 99 data were used for training the network, which had two neurons in the input/points is approximated by regression polynomial of degree k, where k<2N w. Value of this regression polynomial in the point x i substitutes original value y i. Number of data N=1024, width of window N w =50, quadratic polynomial. The SG filtration is /

##### 1 4. Nonstationary Models and Regression In this chapter we examine the problem of finding an appropriate model for data that does not seem to be generated.

)  Z t  {Z t }  WN(0,  2 ), where  (B) and  (B) are different AR polynomials of orders p and P, respectively; and  (B) and  (B) are different MA polynomials of orders q and Q, respectively. The idea here is to try to model the seasonal behavior via the 12 ARMA,  (B s )Y/  2 f t  W t, t=1,…,120. where f t =0, 1 ≤ t ≤ 98, and f t =1, t ≥ 99 (file SBLIN.TSM). Steps in ITSM2000: n Regression > Specify > Poly Regression, order 0 > Include Auxiliary Variables Imported from File > SBLIN.TSM. 22 /

##### ACT – Class Opener:. Recall: Polynomial Function A polynomial function is a function that can be defined by evaluating a polynomial. A function ƒ of one.

2,..., a n are constant coefficients.evaluatingargument Degrees of Polynomial Functions Constant function such as f(x)=a has a degree of zero. Linear functions, f(x) = mx+b, have a degree of one. Quadratic functions have a degree of two. Quadratic Functions: Quadratic Functions All quadratic/ one of the following percent is possible as the percent of 25 words a student defined correctly. Which one is it. A)99% B)80% C)69% D)45% E)26% Writing in Standard Form Write the standard form of the equation of the /

##### Overfitting Overfitting occurs when a statistical model describes random error or noise instead of the underlying relationship. Overfitting generally occurs.

70% accuracy Simple quadratic 90% accuracy Simple linear 90% accuracy Simple quadratic 95% accuracy Simple linear 99% accuracy Simple quadratic 99% accuracy One Solution: Charge Penalty for complex models For example, for the simple {polynomial} classifier, we could charge 1% for every increase in the degree of the polynomial 10 123456789 1 2 3 4 5 6 7 8 9 123456789 1 2 3 4/

##### Foundations of Discrete Mathematics Chapters 5 By Dr. Dalia M. Gil, Ph.D.

sa n-2 = 0, Which can be associated with x 2 – rx - s  This polynomial is called the characteristic polynomial of the recurrence relation The Characteristic Polynomial  Its roots are called the characteristic polynomial roots of the recurrence relation. x 2 – rx - s x 2 – 5x + 6 and characteristic /S = n/2 [2a + (n – 1)d] S = 100/2 [2(-17) + (100 – 1)5] S = 50 [-34 + (99)5] S = 23,050 Arithmetic Sequences  The 100th term of this sequence is a n = a + (n – 1)d a 100 = a + (n – 1)d a 100 = -17 + (100 – 1/

##### Recursion. Recursion: Definition Function that solves a problem by relying on itself to compute the correct solution for a smaller version of the problem.

holds, but breaks around n = 10 C = 1000? C = 1000? 10n 2 +4n+2 < 1000n 10n 2 n n < 99.5 If n = 1 through 99, inequality holds, but breaks around n = 100 Can’t find a n 0 for which it holds for all n >= n 0 Big/many comparisons the minIndex function performs, so the same number of spots in the array are always examined for a given input size. However, reverse sorted data does force more assignments (everything is a new min). Worst Case Selection Adding Polynomials: Adding Polynomials: 3x 3 + 2x + 1 + 2x 3 + /

##### Foundations of Discrete Mathematics Chapters 5 By Dr. Dalia M. Gil, Ph.D.

sa n-2 = 0, Which can be associated with x 2 – rx - s  This polynomial is called the characteristic polynomial of the recurrence relation The Characteristic Polynomial  Its roots are called the characteristic polynomial roots of the recurrence relation. x 2 – rx - s x 2 – 5x + 6 and characteristic /S = n/2 [2a + (n – 1)d] S = 100/2 [2(-17) + (100 – 1)5] S = 50 [-34 + (99)5] S = 23,050 Arithmetic Sequences  The 100th term of this sequence is a n = a + (n – 1)d a 100 = a + (n – 1)d a 100 = -17 + (100 – 1/

##### High-Speed Circuit-Tuning Techniques Based on Lagrangian Relaxation Charlie Chung-Ping Chen ICCAD 99’ Embedded Tutorial Session 12A

reliability Cons –Complicated tool development and support (\$\$) –Tool testing, integration, and training C. Chen, ICCAD ‘99 Embedded Tutorial, Session 12A High-Speed Circuit-Sizing Techniques based on Lagrangian Relaxation Good Tuning Algorithm Fast Optimality /) –No need for sensitization vectors –Solves for all critical paths in a polynomial formulation –False paths; Potentially inaccurate modeling of slopes of input excitation Dynamic Sizing –Simulation based –More accurate –No false path problems /

##### Jian Li Institute of Interdisciplinary Information Sciences Tsinghua University Algorithms for Stochastic Geometric and Combinatorial Optimization Problems.

ε >0  Exact version: find a solution of weight exactly K  Pseudo-polynomial time: polynomial in K  Problems satisfy condition (1): shortest path, minimum spanning tree, matching, knapsack. Our Results If μ is a threshold function, maximizing E[ μ (w(S))] is equivalent to maximizing Pr[w(S)<1] minimizing overflow prob. [Kleinberg, Rabani, Tardos. STOC’97] [Goel, Indyk. FOCS’99] chance-constrained stochastic optimization problem [Swamy/

##### Secret Key Systems (block encoding) Encrypting a small block of text (say 64 bits) General considerations for cipher design:

s 0,2 s 1,2 s 1,3 s 2,3 s 2,0 s 3,0 s 3,1 Secret Key Systems - AES Addition: modulo 2 addition (xor) of polynomials of maximum degree 7 Examples: (x 6 +x 4 +x 2 +x 1 +1) + (x 7 +x 1 +1) = x 7 +x 6 +x 4 +x 2/ c1 1d 9e e e1 f8 98 11 69 d9 8e 94 9b 1e 87 e9 ce 55 28 df f 8c a1 89 0d bf e6 42 68 41 99 2d 0f b0 54 bb 16 Secret Key Systems - AES The Inverse S-Box: y 0 1 2 3 4 5 6 7 8 9 a b c d e/

##### Next-Generation Bioinformatics Systems Jelena Kovačević Center for Bioimage Informatics Department of Biomedical Engineering Carnegie Mellon University.

Technology Evaluation FpVTE 2003 48,105 sets, 25,309 individuals, 393,370 distinct fingerprints Verification results 99.4% true accept rate @ 0.01% false accept rate 99.9% true accept rate @ 1.0% false accept rate Challenges Poor-quality images Database size /, add equal norm tight ENMR Construction by seeding Construction by seeding 01n-1 Tools: Polynomial algebras and transforms Tools: Polynomial algebras and transforms m S 79 Invariance of Frame Properties FA B is FA, B invertible 0 0 MR F A is MRFA/

##### Wouter Verkerke (University of California Santa Barbara / NIKHEF)

N>10) Wouter Verkerke, UCSB Properties of the Gaussian distribution Mean and Variance Integrals of Gaussian 68.27% within 1s 90%  1.645s 95.43% within 2s 95%  1.96s 99.73% within 3s 99%  2.58s 99.9%  3.29s Wouter Verkerke, / 0.96156 -0.681 0.127 -0.895 1.000 Wouter Verkerke, UCSB Mitigating fit stability problems -- Polynomials Warning: Regular parameterization of polynomials a0+a1x+a2x2+a3x3 nearly always results in strong correlations between the coefficients ai. Fit stability problems, inability to/

##### Curving Fitting with 6-9 Polynomial Functions Warm Up

8 Third differences: 0.6 1 0.6 0.8 0.8Close Check It Out! Example 2 Continued Step 2 Determine the degree of the polynomial. Because the third differences are relatively close, a cubic function should be a good model. Step 3 Use the cubic regression feature on/)2 – 858.99(6) + 693.88 Based on the model, the opening value was about \$2563.18 in 2000. Check It Out! Example 3 The table below shows the opening value of a stock index on the first day of trading in various years. Use a polynomial model to estimate /

##### Curving Fitting with 6-9 Polynomial Functions Warm Up

8 Third differences: 0.6 1 0.6 0.8 0.8Close Check It Out! Example 2 Continued Step 2 Determine the degree of the polynomial. Because the third differences are relatively close, a cubic function should be a good model. Step 3 Use the cubic regression feature on/)2 – 858.99(6) + 693.88 Based on the model, the opening value was about \$2563.18 in 2000. Check It Out! Example 3 The table below shows the opening value of a stock index on the first day of trading in various years. Use a polynomial model to estimate /

##### Theoretical Cryptography Lecture 1: Introduction, Standard Model of Cryptography, Identification, One-way functions Lecturer: Moni Naor Weizmann Institute.

Circular encryption.... Attacks outside standard model: Timing attacks [Kocher 96] Fault detection [BDL 97, BS 97] Power analysis [KJJ 99] Cache attacks [OST 05] Memory attacks [HSHCPCFAF 08]... Adversarial Models Attacks - standard model: Chosen-plaintext attacks Chosen-ciphertext attacks Composition/A function f:{0,1} n → {0,1} n is called a (t,ε) one-way function, if f is a polynomial-time computable function (independent of t) for every t-time algorithm A, Prob[A(f(x))  f -1 (f(x)) ] ≤ ε Where /

##### CHAPTER 5: Public-key cryptography

Informally, a function F:N -> N is said to be one-way function if it is easily computable - in polynomial time - but any computation of its inverse is infeasible. A one-way permutation is a 1-1 one-way function. easy x f(x) computation/seems to be infeasible. Example If A = (74, 82,94, 83, 39, 99, 56, 49, 73, 99) and B = (1100110101) then ABT = Public-key cryptography Another view of the knapsack problem IV054 Another view of the knapsack problem Each knapsack vector A = (a1,…,an) defines an integer valued /

##### 1. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Polynomials CHAPTER 5.1Exponents and Scientific Notation 5.2Introduction.

Pearson Education, Inc. Publishing as Pearson Addison-Wesley The product of two binomials can be shown in terms of geometry. 35 5x5x 7x7xx2x2 Length width = Sum of the areas of the four internal rectangles Combine like terms. Slide 5- 98 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 3 Multiply polynomials. Slide 5- 99 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison/

##### Ch 4: Polynomials Polynomials Algebra Polynomial ideals.

We introduce infinite dimensional algebra (purely abstract device) (fg)h=f(gh) Algebra of formal power series deg f: Scalar polynomial cx 0 Monic polynomial f n = 1. Theorem 1: f, g nonzero polynomials over F. Then 1.fg is nonzero. 2.deg(fg)=deg f + deg/. This is the Lagrange interpolation formula. –This follows from Theorem 15. P.99. (a->f, f i ->L i,a i ->P i ) Example: Let f = x j. Then Bases The change of basis matrix is invertible (The points are distinct.) Vandermonde matrix Linear algebra isomorphism/

##### TEMPLATE DESIGN © 2008 www.PosterPresentations.com Assessing the Potential of the AIRS Retrieved Surface Temperature for 6-Hour Average Temperature Forecast.

16 0.01 0.68 0.31 0.34 0.66 0.01 0.99 53% 0.85 0.15 0.01 0.68 0.31 0.34 0.66 0.01 0.99 67% 0.85 0.15 0.01 0.68 0.31 0.34 /0.66 0.01 0.99 80% 0.84 0.16 0.01 0.67 0.32 0.33 0.66 0.01 0.99 Statistic Numbers ( 0 K) CNRFC 1200-1800 1800-0000 0000-0600 0600-1200/ 1.97 Larger bias and error at 18-00Z and 06-12Z 3-day (April 14-16, 2011) daily cycle of basin averaged hourly temperature (generated by GES-DISC Giovanni) Try polynomial fit 00-06, 06-12, and 12-18Z: T ave = a*T des + b*T asc + c /

##### Short Course Spectral-element solution of the elastic wave equation Andreas Fichtner.

of the collocation points: Interpolation of Runge‘s function R(x) using 6 th -order polynomials and Gauss-Lobatto-Legendre collocation points [ roots of (1-x 2 )Lo N-1 = completed Lobatto polynomial ] interpolant We should use the GLL points as collocation points for the Lagrange polynomials. SPECTRAL-ELEMENT METHOD: General Concept Example: GLL Lagrange polynomials of/ with the upper layer of elements … … and PREM below boundary between the upper 2 layers of elements lon=142.74° lat=-5.99° d=80 km SA08/