Hardness Amplification of Optimization Problems

In this paper, we prove a general hardness amplification scheme for optimization problems based on the technique of direct products. We say that an optimization problem ? is direct product feasible if it is possible to efficiently aggregate any k instances of ? and form one large instance of ? such that given an optimal feasible solution to the larger instance, we can efficiently find optimal feasible solutions to all the k smaller instances. Given a direct product feasible optimization problem ?, our hardness amplification theorem may be informally stated as follows: If there is a distribution D over instances of ? of size n such that every randomized algorithm running in time t(n) fails to solve ? on 1/?(n) fraction of inputs sampled from D, then, assuming some relationships on ?(n) and t(n), there is a distribution D\u27 over instances of ? of size O(n??(n)) such that every randomized algorithm running in time t(n)/poly(?(n)) fails to solve ? on 99/100 fraction of inputs sampled from D\u27. As a consequence of the above theorem, we show hardness amplification of problems in various classes such as NP-hard problems like Max-Clique, Knapsack, and Max-SAT, problems in P such as Longest Common Subsequence, Edit Distance, Matrix Multiplication, and even problems in TFNP such as Factoring and computing Nash equilibrium

Particle displacements in the elastic deformation of amorphous materials: local fluctuations vs. non-affine field

We study the local disorder in the deformation of amorphous materials by decomposing the particle displacements into a continuous, inhomogeneous field and the corresponding fluctuations. We compare these fields to the commonly used non-affine displacements in an elastically deformed 2D Lennard-Jones glass. Unlike the non-affine field, the fluctuations are very localized, and exhibit a much smaller (and system size independent) correlation length, on the order of a particle diameter, supporting the applicability of the notion of local "defects" to such materials. We propose a scalar "noise" field to characterize the fluctuations, as an additional field for extended continuum models, e.g., to describe the localized irreversible events observed during plastic deformation.Comment: Minor corrections to match the published versio

On Ladder Logic Bombs in Industrial Control Systems

In industrial control systems, devices such as Programmable Logic Controllers (PLCs) are commonly used to directly interact with sensors and actuators, and perform local automatic control. PLCs run software on two different layers: a) firmware (i.e. the OS) and b) control logic (processing sensor readings to determine control actions). In this work, we discuss ladder logic bombs, i.e. malware written in ladder logic (or one of the other IEC 61131-3-compatible languages). Such malware would be inserted by an attacker into existing control logic on a PLC, and either persistently change the behavior, or wait for specific trigger signals to activate malicious behaviour. For example, the LLB could replace legitimate sensor readings with manipulated values. We see the concept of LLBs as a generalization of attacks such as the Stuxnet attack. We introduce LLBs on an abstract level, and then demonstrate several designs based on real PLC devices in our lab. In particular, we also focus on stealthy LLBs, i.e. LLBs that are hard to detect by human operators manually validating the program running in PLCs. In addition to introducing vulnerabilities on the logic layer, we also discuss countermeasures and we propose two detection techniques.Comment: 11 pages, 14 figures, 2 tables, 1 algorith

A study of the dynamics of rotating space stations with elastically connected counterweight and attached flexible appendages. Volume 1: Theory

The formulation of a mathematical model for predicting the dynamic behavior of rotating flexible space station configurations was conducted. The overall objectives of the study were: (1) to develop the theoretical techniques for determining the behavior of a realistically modeled rotating space station, (2) to provide a versatile computer program for the numerical analysis, and (3) to present practical concepts for experimental verification of the analytical results. The mathematical model and its associated computer program are described

The brattleboro rat displays a natural deficit in social discrimination that is restored by clozapine and a neurotensin analog.

Cognitive deficits in schizophrenia are a major source of dysfunction for which more effective treatments are needed. The vasopressin-deficient Brattleboro (BRAT) rat has been shown to have several natural schizophrenia-like deficits, including impairments in prepulse inhibition and memory. We investigated BRAT rats and their parental strain, Long-Evans (LE) rats, in a social discrimination paradigm, which is an ethologically relevant animal test of cognitive deficits of schizophrenia based upon the natural preference of animals to investigate conspecifics. We also investigated the effects of the atypical antipsychotic, clozapine, and the putative antipsychotic, PD149163, a brain-penetrating neurotensin-1 agonist, on social discrimination in these rats. Adult rats were administered saline or one of the three doses of clozapine (0.1, 1.0, or 10 mg/kg) or PD149163 (0.1, 0.3, or 1.0 mg/kg), subcutaneously. Following drug administration, adult rats were exposed to a juvenile rat for a 4-min learning period. Animals were then housed individually for 30 min and then simultaneously exposed to the juvenile presented previously and a new juvenile for 4 min. Saline-treated LE rats, but not BRAT rats, exhibited intact social discrimination as evidenced by greater time spent exploring the new juvenile. The highest dose of clozapine and the two highest doses of PD149163 restored social discrimination in BRAT rats. These results provide further support for the utility of the BRAT rat as a genetic animal model relevant to schizophrenia and drug discovery. The potential of neurotensin agonists as putative treatments for cognitive deficits of schizophrenia was also supported

Towards a General Direct Product Testing Theorem

The Direct Product encoding of a string a in {0,1}^n on an underlying domain V subseteq ([n] choose k), is a function DP_V(a) which gets as input a set S in V and outputs a restricted to S. In the Direct Product Testing Problem, we are given a function F:V -> {0,1}^k, and our goal is to test whether F is close to a direct product encoding, i.e., whether there exists some a in {0,1}^n such that on most sets S, we have F(S)=DP_V(a)(S). A natural test is as follows: select a pair (S,S\u27)in V according to some underlying distribution over V x V, query F on this pair, and check for consistency on their intersection. Note that the above distribution may be viewed as a weighted graph over the vertex set V and is referred to as a test graph. The testability of direct products was studied over various domains and test graphs: Dinur and Steurer (CCC \u2714) analyzed it when V equals the k-th slice of the Boolean hypercube and the test graph is a member of the Johnson graph family. Dinur and Kaufman (FOCS \u2717) analyzed it for the case where V is the set of faces of a Ramanujan complex, where in this case V=O_k(n). In this paper, we study the testability of direct products in a general setting, addressing the question: what properties of the domain and the test graph allow one to prove a direct product testing theorem? Towards this goal we introduce the notion of coordinate expansion of a test graph. Roughly speaking a test graph is a coordinate expander if it has global and local expansion, and has certain nice intersection properties on sampling. We show that whenever the test graph has coordinate expansion then it admits a direct product testing theorem. Additionally, for every k and n we provide a direct product domain V subseteq (n choose k) of size n, called the Sliding Window domain for which we prove direct product testability