Computation-Communication Trade-offs and Sensor Selection in Real-time Estimation for Processing Networks

Recent advances in electronics are enabling substantial processing to be performed at each node (robots, sensors) of a networked system. Local processing enables data compression and may mitigate measurement noise, but it is still slower compared to a central computer (it entails a larger computational delay). However, while nodes can process the data in parallel, the centralized computational is sequential in nature. On the other hand, if a node sends raw data to a central computer for processing, it incurs communication delay. This leads to a fundamental communication-computation trade-off, where each node has to decide on the optimal amount of preprocessing in order to maximize the network performance. We consider a network in charge of estimating the state of a dynamical system and provide three contributions. First, we provide a rigorous problem formulation for optimal real-time estimation in processing networks in the presence of delays. Second, we show that, in the case of a homogeneous network (where all sensors have the same computation) that monitors a continuous-time scalar linear system, the optimal amount of local preprocessing maximizing the network estimation performance can be computed analytically. Third, we consider the realistic case of a heterogeneous network monitoring a discrete-time multi-variate linear system and provide algorithms to decide on suitable preprocessing at each node, and to select a sensor subset when computational constraints make using all sensors suboptimal. Numerical simulations show that selecting the sensors is crucial. Moreover, we show that if the nodes apply the preprocessing policy suggested by our algorithms, they can largely improve the network estimation performance.Comment: 15 pages, 16 figures. Accepted journal versio

Safe Recursion on Notation into a Light Logic by Levels

We embed Safe Recursion on Notation (SRN) into Light Affine Logic by Levels (LALL), derived from the logic L4. LALL is an intuitionistic deductive system, with a polynomial time cut elimination strategy. The embedding allows to represent every term t of SRN as a family of proof nets |t|^l in LALL. Every proof net |t|^l in the family simulates t on arguments whose bit length is bounded by the integer l. The embedding is based on two crucial features. One is the recursive type in LALL that encodes Scott binary numerals, i.e. Scott words, as proof nets. Scott words represent the arguments of t in place of the more standard Church binary numerals. Also, the embedding exploits the "fuzzy" borders of paragraph boxes that LALL inherits from L4 to "freely" duplicate the arguments, especially the safe ones, of t. Finally, the type of |t|^l depends on the number of composition and recursion schemes used to define t, namely the structural complexity of t. Moreover, the size of |t|^l is a polynomial in l, whose degree depends on the structural complexity of t. So, this work makes closer both the predicative recursive theoretic principles SRN relies on, and the proof theoretic one, called /stratification/, at the base of Light Linear Logic

Tunable zero and first sounds in ultracold Fermi gases with Rabi coupling

We consider a weakly-interacting fermionic gas of alkali-metal atoms characterized by two hyper- fine states which are Rabi coupled. By using a Hartree approximation for the repulsive interaction we determine the zero-temperature equation of state of this Fermi gas in D spatial dimensions (D = 1, 2, 3). Then, adopting the Landau-Vlasov equation and hydrodynamic equations, we investi- gate the speed of first sound and zero sound. We show that the two sounds, which occur respectively in collisional and collisionless regimes, crucially depend on the interplay between interaction strength and Rabi coupling. Finally, we discuss for some experimentally relevant cases the effect of a trapping harmonic potential on the density profiles of the fermionic system.Comment: Accepted in Journal of Statistical Mechanic

Quantum bright solitons in a quasi-one-dimensional optical lattice

We study a quasi-one-dimensional attractive Bose gas confined in an optical lattice with a superimposed harmonic potential by analyzing the effective one-dimensional Bose-Hubbard Hamiltonian of the system. In order to have a reliable description of the ground-state, that we call quantum bright soliton, we use the Density-Matrix-Renormalization-Group (DMRG) technique. By comparing DMRG results with mean-field (MF) ones we find that beyond-mean-field effects become relevant by increasing the attraction between bosons or by decreasing the frequency of the harmonic confinement. In particular we discover that, contrary to the MF predictions based on the discrete nonlinear Schr\"odinger equation, quantum bright solitons are not self-trapped. We also use the time-evolving-block-decimation (TEBD) method to investigate dynamical properties of bright solitons when the frequency of the harmonic potential is suddenly increased. This quantum quench induces a breathing mode whose period crucially depends on the final strength of the super-imposed harmonic confinement

Economic Factors of Vulnerability Trade and Exploitation

Cybercrime markets support the development and diffusion of new attack technologies, vulnerability exploits, and malware. Whereas the revenue streams of cyber attackers have been studied multiple times in the literature, no quantitative account currently exists on the economics of attack acquisition and deployment. Yet, this understanding is critical to characterize the production of (traded) exploits, the economy that drives it, and its effects on the overall attack scenario. In this paper we provide an empirical investigation of the economics of vulnerability exploitation, and the effects of market factors on likelihood of exploit. Our data is collected first-handedly from a prominent Russian cybercrime market where the trading of the most active attack tools reported by the security industry happens. Our findings reveal that exploits in the underground are priced similarly or above vulnerabilities in legitimate bug-hunting programs, and that the refresh cycle of exploits is slower than currently often assumed. On the other hand, cybercriminals are becoming faster at introducing selected vulnerabilities, and the market is in clear expansion both in terms of players, traded exploits, and exploit pricing. We then evaluate the effects of these market variables on likelihood of attack realization, and find strong evidence of the correlation between market activity and exploit deployment. We discuss implications on vulnerability metrics, economics, and exploit measurement.Comment: 17 pages, 11 figures, 14 table

A comparison of four different methods to estimate population size of Alpine marmot (Marmota marmota)

Obtaining reliable information on animal abundance in mountainous landscapes is challenging. Highly heterogeneous habitats tend to reduce detection probabilities, and the three-dimensional, rugged nature of the terrain poses severe limits to the fulfilment of a number of assumptions underlying several statistical methods. In this study, we aimed to compare the performance of 4 different methods to estimate population size of Alpine marmot (Marmota marmota), a highly social semifossorial rodent widely distributed on the European Alps. Between May and August 2015, in a study area within the Stelvio National Park (Italy) we conducted 8 sessions of capture-mark-recapture, 6 sessions of mark-resight from vantage points, 8 sessions of line distance sampling along 4 transects, and 2 sessions using double-observer methods from vantage points. The minimum number of animals alive, obtained during the mark-resight surveys, was n=54 individuals. Capture-mark-recapture models estimated a population size of n=56 individuals [95% CI (45,87)]; similar, but more precise estimates were obtained with the mark-resight approach {Bowden’s estimator: n=62 [95% CI (54,71)]; Poisson log-normal estimator: n=62 [95% CI (55,69)]}. Line distance sampling and double-observer methods were severely biased low {Line distance sampling: n=24 individuals [95% CI (19,31)]; Independent double-observer: n=24 [95% CI (22, 35)]; Dependent double-observer: n=15 [95% CI (15,20)]}. Our results suggest that the probabilistic approach based on marked individuals yielded fairly robust estimates of population size. The underestimates obtained using distance sampling and double-observer methods were likely due to the violation of some underlying assumptions. While the topography of the mountainous landscape makes it difficult to randomize the sampling scheme, the semifossorial behaviour of the target species is likely to lower the detection probabilities and violate the assumption of perfect detection on the transect

Rich, Sturmian, and trapezoidal words

In this paper we explore various interconnections between rich words, Sturmian words, and trapezoidal words. Rich words, first introduced in arXiv:0801.1656 by the second and third authors together with J. Justin and S. Widmer, constitute a new class of finite and infinite words characterized by having the maximal number of palindromic factors. Every finite Sturmian word is rich, but not conversely. Trapezoidal words were first introduced by the first author in studying the behavior of the subword complexity of finite Sturmian words. Unfortunately this property does not characterize finite Sturmian words. In this note we show that the only trapezoidal palindromes are Sturmian. More generally we show that Sturmian palindromes can be characterized either in terms of their subword complexity (the trapezoidal property) or in terms of their palindromic complexity. We also obtain a similar characterization of rich palindromes in terms of a relation between palindromic complexity and subword complexity.Comment: 7 page

Quantum Programming Made Easy

We present IQu, namely a quantum programming language that extends Reynold's Idealized Algol, the paradigmatic core of Algol-like languages. IQu combines imperative programming with high-order features, mediated by a simple type theory. IQu mildly merges its quantum features with the classical programming style that we can experiment through Idealized Algol, the aim being to ease a transition towards the quantum programming world. The proposed extension is done along two main directions. First, IQu makes the access to quantum co-processors by means of quantum stores. Second, IQu includes some support for the direct manipulation of quantum circuits, in accordance with recent trends in the development of quantum programming languages. Finally, we show that IQu is quite effective in expressing well-known quantum algorithms.Comment: In Proceedings Linearity-TLLA 2018, arXiv:1904.0615

Enumeration and Structure of Trapezoidal Words

Trapezoidal words are words having at most $n+1$ distinct factors of length $n$ for every $n\ge 0$. They therefore encompass finite Sturmian words. We give combinatorial characterizations of trapezoidal words and exhibit a formula for their enumeration. We then separate trapezoidal words into two disjoint classes: open and closed. A trapezoidal word is closed if it has a factor that occurs only as a prefix and as a suffix; otherwise it is open. We investigate open and closed trapezoidal words, in relation with their special factors. We prove that Sturmian palindromes are closed trapezoidal words and that a closed trapezoidal word is a Sturmian palindrome if and only if its longest repeated prefix is a palindrome. We also define a new class of words, \emph{semicentral words}, and show that they are characterized by the property that they can be written as $uxyu$, for a central word $u$ and two different letters $x,y$. Finally, we investigate the prefixes of the Fibonacci word with respect to the property of being open or closed trapezoidal words, and show that the sequence of open and closed prefixes of the Fibonacci word follows the Fibonacci sequence.Comment: Accepted for publication in Theoretical Computer Scienc