Eigenvalues of block structured asymmetric random matrices

We study the spectrum of an asymmetric random matrix with block structured variances. The rows and columns of the random square matrix are divided into $D$ partitions with arbitrary size (linear in $N$). The parameters of the model are the variances of elements in each block, summarized in $g\in\mathbb{R}^{D\times D}_+$. Using the Hermitization approach and by studying the matrix-valued Stieltjes transform we show that these matrices have a circularly symmetric spectrum, we give an explicit formula for their spectral radius and a set of implicit equations for the full density function. We discuss applications of this model to neural networks

The Topology of Wireless Communication

In this paper we study the topological properties of wireless communication maps and their usability in algorithmic design. We consider the SINR model, which compares the received power of a signal at a receiver against the sum of strengths of other interfering signals plus background noise. To describe the behavior of a multi-station network, we use the convenient representation of a \emph{reception map}. In the SINR model, the resulting \emph{SINR diagram} partitions the plane into reception zones, one per station, and the complementary region of the plane where no station can be heard. We consider the general case where transmission energies are arbitrary (or non-uniform). Under that setting, the reception zones are not necessarily convex or even connected. This poses the algorithmic challenge of designing efficient point location techniques as well as the theoretical challenge of understanding the geometry of SINR diagrams. We achieve several results in both directions. We establish a form of weaker convexity in the case where stations are aligned on a line. In addition, one of our key results concerns the behavior of a $(d+1)$-dimensional map. Specifically, although the $d$-dimensional map might be highly fractured, drawing the map in one dimension higher "heals" the zones, which become connected. In addition, as a step toward establishing a weaker form of convexity for the $d$-dimensional map, we study the interference function and show that it satisfies the maximum principle. Finally, we turn to consider algorithmic applications, and propose a new variant of approximate point location.Comment: 64 pages, appeared in STOC'1

Aquatic-Terrestrial Linkages: Formation, Importance, and Disruption

We can no longer regard ecosystems as discrete entities in space. Similar to human societies, the natural environment is a product of a wide range of transport, propagation, and communication processes. Spatial coupling of ecosystems through cross-habitat fluxes of energy and matter may modify food web interactions, change ecosystem function, and alter community diversity. Lateral fluxes of matter and energy between discrete ecosystems have been shown to elicit variable responses in the recipient ones depending on trophic position, ecological process, biotic and abiotic conditions, and the ratio between the subsidy and local resources. In some cases, cross ecosystem nutrient fluxes can be as important as transfers within individual ecosystems. Some of the best documented ecosystem linkages occur in aquatic-terrestrial systems. For example, terrestrial animals feeding in freshwater and marine habitats transfer nutrients from these aquatic to adjacent terrestrial ecosystems leading to increases in primary production in the latter. Such increases in production are comparable in magnitude to positive effects of moderately elevated local herbivory observed in some systems or nitrogen fixation by alder. Nonetheless, recent human-induced ecosystem alterations result in disruption of the spatial continuity of ecosystem linkages. Here I evaluate the current knowledge on the formation and importance of aquatic-terrestrial linkages and provide examples of the consequences of discontinuity in these transport processes

Seasonal diets of mink and martens: Effects of spatial and temporal changes in resource abundance

Thesis (Ph.D.) University of Alaska Fairbanks, 1996Seasonal changes in food availability and feeding habits of mink (Mustela vison) and martens (Martes americana) on Chichagof Island, Southeast Alaska, were studied through the analysis of natural abundance of stable isotopes. Dependence of the two species on marine-derived nutrients, carried to the terrestrial system via the upstream migration of spawning Pacific salmon (Onchorhynchus sp.), was investigated. Twenty-four mink and 75 martens were live-trapped repeatedly in early summer (prior to salmon runs), early autumn (post salmon runs), late winter, and in spring (during the mating season). A blood sample was obtained from each individual. In addition, 25 mink and 165 marten carcasses were obtained from trappers during late autumn 1991-1994. Concurrently, prey availability was monitored, and tissues from prey were collected. The abundance of stable isotopes in prey tissues and blood samples were compared, indicating that riverine mink depended on salmon (carcasses and fry), with little seasonal or individual variation, whereas coastal mink relied on intertidal organisms in spring and summer, but fed on salmon carcasses when they became available in autumn. In addition, analysis of blood progesterone revealed that timing of reproduction in female mink appear to be shifted, so that lactation coincided with the availability of salmon carcasses. In contrast, martens showed individual variation in their diets, with some individuals feeding exclusively on terrestrial organisms, while the diets of others include salmon carcasses. Incorporation of salmon in the diet depended largely on availability of small rodents and location of the martens home range on the landscape. Although salmon carcasses are not a preferred food item for martens, they act as a suitable alternative to maintain body condition and allow successful reproduction even in years when preferred food is not readily available

Secluded Connectivity Problems

Consider a setting where possibly sensitive information sent over a path in a network is visible to every {neighbor} of the path, i.e., every neighbor of some node on the path, thus including the nodes on the path itself. The exposure of a path $P$ can be measured as the number of nodes adjacent to it, denoted by $N[P]$. A path is said to be secluded if its exposure is small. A similar measure can be applied to other connected subgraphs, such as Steiner trees connecting a given set of terminals. Such subgraphs may be relevant due to considerations of privacy, security or revenue maximization. This paper considers problems related to minimum exposure connectivity structures such as paths and Steiner trees. It is shown that on unweighted undirected $n$-node graphs, the problem of finding the minimum exposure path connecting a given pair of vertices is strongly inapproximable, i.e., hard to approximate within a factor of $O(2^{\log^{1-\epsilon}n})$ for any $\epsilon>0$ (under an appropriate complexity assumption), but is approximable with ratio $\sqrt{\Delta}+3$, where $\Delta$ is the maximum degree in the graph. One of our main results concerns the class of bounded-degree graphs, which is shown to exhibit the following interesting dichotomy. On the one hand, the minimum exposure path problem is NP-hard on node-weighted or directed bounded-degree graphs (even when the maximum degree is 4). On the other hand, we present a polynomial algorithm (based on a nontrivial dynamic program) for the problem on unweighted undirected bounded-degree graphs. Likewise, the problem is shown to be polynomial also for the class of (weighted or unweighted) bounded-treewidth graphs

Generalized Perron--Frobenius Theorem for Nonsquare Matrices

The celebrated Perron--Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. However, many real-life scenarios give rise to nonsquare matrices. A natural question is whether the PF Theorem (along with its applications) can be generalized to a nonsquare setting. Our paper provides a generalization of the PF Theorem to nonsquare matrices. The extension can be interpreted as representing client-server systems with additional degrees of freedom, where each client may choose between multiple servers that can cooperate in serving it (while potentially interfering with other clients). This formulation is motivated by applications to power control in wireless networks, economics and others, all of which extend known examples for the use of the original PF Theorem. We show that the option of cooperation between servers does not improve the situation, in the sense that in the optimal solution no cooperation is needed, and only one server needs to serve each client. Hence, the additional power of having several potential servers per client translates into \emph{choosing} the best single server and not into \emph{sharing} the load between the servers in some way, as one might have expected. The two main contributions of the paper are (i) a generalized PF Theorem that characterizes the optimal solution for a non-convex nonsquare problem, and (ii) an algorithm for finding the optimal solution in polynomial time

Preventing malaria in international travellers: an evaluation of published English-language guidelines

Background People intending to travel may seek information on malaria prevention from a range of sources. To ensure the best protection, this information needs to be reliable, up-to-date, consistent, and useful to their decision making. This study appraises current international and national guidelines written in English for malaria prevention in travellers, and whether any recommendations conflict. Methods We systematically identified national or international English-language guidelines on malaria prevention in travellers to July 2013 using standard and multiple searching methods. We critically appraised guidelines using the AGREE II tool, and report inconsistent recommendations within guidelines. Results We identified five sets of English-language guidelines on preventing malaria for travellers. Assessment against AGREE II indicate that all of the guidelines fall short of internationally accepted standards in guideline development: none include a transparent description of methods; only one describes sources of funding or potential conflicts of interest; and only one includes formal presentation of the evidence alongside transparent assessment of the quality of that evidence. There were a number of important discrepancies between guidelines, and some omit information about effectiveness, safety and adverse effects of chemoprophylaxis options. Conclusions The methods used for developing guidelines for malaria prevention in travellers lags behind current internationally recognized standards. Healthcare professionals as well as travellers themselves could be better informed if guidelines were more systematic and transparent summaries of the current knowledge on drug interventions in relation to effects, safety, administration and contra-indications