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In standard clustering problems, data points are represented by vectors, and by stacking them together, one forms a data matrix with row or column cluster structure. In this paper, we consider a class of binary matrices, arising in many applications, which exhibit both row and column cluster structure, and our goal is to exactly recover the underlying row and column clusters by observing only a small fraction of noisy entries. We first derive a lower bound on the minimum number of observations needed for exact cluster recovery. Then, we propose three algorithms with different running time and compare the number of observations needed by them for successful cluster recovery. Our analytical results show smooth time-data trade-offs: one can gradually reduce the computational complexity when increasingly more observations are available.

We find an optimal upper bound on the values of the weak$^*$-dentability index $Dz(X)$ in terms of the Szlenk index $Sz(X)$ of a Banach space $X$ with separable dual. Namely, if $\;Sz(X)=\omega^{\alpha}$, for some $\alpha<\omega_1$, and $p\in(1,\infty)$, then $$Sz(X)\le Dz(X)\le Sz(L_p(X))\le {cases} \omega^{\alpha+1} &\text{if $\alpha$ is a finite ordinal,} \omega^{\alpha} &\text{if $\alpha$ is an infinite ordinal.} {cases}$$

This paper presents an asynchronous distributed algorithm to manage multiple trees for peer-to-peer streaming in a flow level model. It is assumed that videos are cut into substreams, with or without source coding, to be distributed to all nodes. The algorithm guarantees that each node receives sufficiently many substreams within delay logarithmic in the number of peers. The algorithm works by constantly updating the topology so that each substream is distributed through trees to as many nodes as possible without interference. Competition among trees for limited upload capacity is managed so that both coverage and balance are achieved. The algorithm is robust in that it efficiently eliminates cycles and maintains tree structures in a distributed way. The algorithm favors nodes with higher degree, so it not only works for live streaming and video on demand, but also in the case a few nodes with large degree act as servers and other nodes act as clients. A proof of convergence of the algorithm is given assuming instantaneous update of depth information, and for the case of a single tree it is shown that the convergence time is stochastically tightly bounded by a small constant times the log of the number of nodes. These theoretical results are complemented by simulations showing that the algorithm works well even when most assumptions for the theoretical tractability do not hold.

We study the content placement problem for cache delivery video-on-demand systems under static random network topologies with fixed heavy-tailed video demand. The performance measure is the amount of server load; we wish to minimize the total download rate for all users from the server and maximize the rate from caches. Our approach reduces the analysis for multiple videos to consideration of decoupled systems with a single video each. For each placement policy, insights gained from the single video analysis carry back to the original multiple video content placement problem. Finally, we propose a hybrid placement technique that achieves near optimal performance with low complexity.

We consider a model of a decentralized multiple access system with a non-standard binary feedback where the empty and collision situations cannot be distinguished. We show that, like in the case of a ternary feedback, for any input rate \lambda < 1/e, there exists a "doubly randomized" adaptive transmission protocol which stabilizes the behavior of the system. We discuss also a number of related problems and formulate some hypotheses., Comment: 11 pages, ! figure

Within the possibilistic approach to uncertainty modeling, the paper presents a modal logical system to reason about qualitative (comparative) statements of the possibility (and necessity) of fuzzy propositions. We relate this qualitative modal logic to the many--valued analogues MVS5 and MVKD45 of the well known modal logics of knowledge and belief S5 and KD45 respectively. Completeness results are obtained for such logics and therefore, they extend previous existing results for qualitative possibilistic logics in the classical non-fuzzy setting., Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI1994)

In this paper we deal with a new approach to probabilistic reasoning in a logical framework. Nearly almost all logics of probability that have been proposed in the literature are based on classical two-valued logic. After making clear the differences between fuzzy logic and probability theory, here we propose a {em fuzzy} logic of probability for which completeness results (in a probabilistic sense) are provided. The main idea behind this approach is that probability values of crisp propositions can be understood as truth-values of some suitable fuzzy propositions associated to the crisp ones. Moreover, suggestions and examples of how to extend the formalism to cope with conditional probabilities and with other uncertainty formalisms are also provided., Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995)

Within a 1.5 year comprehensive fading experiment several batches of LiF:Mg,Ti and LiF:Mg,Cu,P thermoluminescence detectors (TLDs) were studied. The TLDs originated from two manufacturers and were processed by three laboratories using different annealing and readout conditions. The TLDs were irradiated with two radiation modalities (gamma-rays and thermal neutrons) and were stored at two temperatures (-17.4C and +18.5C). The goal of the experiment was to verify the stability of TLDs in the context of their application in long-term measurements in space. The results revealed that the response of all TLDs is stable within 10% for the studied temperature range. No influence of the radiation type was found. These results indicate that for the properly oven-annealed LiF TLDs, fading is not a significant problem, even for measuring periods longer than a year.

Recent spectrum auctions in the United Kingdom, and some proposals for future auctions of spectrum in the United States, are based on preliminary price discovery rounds, followed by calculation of final prices for the winning buyers. For example, the prices could be the projection of Vikrey prices onto the core of reported prices. The use of Vikrey prices should lead to more straightforward bidding, but the projection reverses some of the incentive for bidders to report truthfully. Still, we conjecture that the price paid by a winning buyer increases no faster than the bid, as in a first price auction. It would be rather disturbing if the conjecture is false. The conjecture is established for a buyer interacting with disjoint groups of other buyers in a star network setting. It is also shown that for any core-selecting payment rule and any integer w greater than or equal to two, there is a market setting with w winning buyers such that the price paid by some winning buyer increases at least (1-1/w) times as fast as the price bid., Comment: 8 pages, 2 figures. This work was presented at the Workshop on Telecom Economics, Engineering and Policy 2012, Krakow, Poland

A typical result in this note is that if $X$ is a Banach space which is a weak Asplund space and has the $\omega^*$-$\omega$-Kadets Klee property, then $X$ is already an Asplund space.

A supermarket game is considered with $N$ FCFS queues with unit exponential service rate and global Poisson arrival rate $N \lambda$. Upon arrival each customer chooses a number of queues to be sampled uniformly at random and joins the least loaded sampled queue. Customers are assumed to have cost for both waiting and sampling, and they want to minimize their own expected total cost. We study the supermarket game in a mean field model that corresponds to the limit as $N$ converges to infinity in the sense that (i) for a fixed symmetric customer strategy, the joint equilibrium distribution of any fixed number of queues converges as $N \to \infty$ to a product distribution determined by the mean field model and (ii) a Nash equilibrium for the mean field model is an $\epsilon$-Nash equilibrium for the finite $N$ model with $N$ sufficiently large. It is shown that there always exists a Nash equilibrium for $\lambda <1$ and the Nash equilibrium is unique with homogeneous waiting cost for $\lambda^2 \le 1/2$. Furthermore, we find that the action of sampling more queues by some customers has a positive externality on the other customers in the mean field model, but can have a negative externality for finite $N$., Comment: Submitted to Stochastic Systems

DeMarzo et al. (2005) consider auctions in which bids are selected from a completely ordered family of securities whose values are tied to the resource being auctioned. The paper defines a notion of relative steepness of families of securities and shows that a steeper family provides greater expected revenue to the seller. Two assumptions are: the buyers are risk-neutral; the random variables through which values and signals of the buyers are realized are affiliated. We show that this revenue ranking holds for the second price auction in the case of risk-aversion. However, it does not hold if affiliation is relaxed to a less restrictive form of positive dependence, namely first order stochastic dominance (FOSD). We define the relative strong steepness of families of securities and show that it provides a necessary and sufficient condition for comparing two families in the FOSD case. All results extend to the English auction., Comment: 21 pages, 3 figures. This is a work in progress

This paper focuses on the stationary portion of file download in an unstructured peer-to-peer network, which typically follows for many hours after a flash crowd initiation. The model includes the case that peers can have some pieces at the time of arrival. The contribution of the paper is to identify how much help is needed from the seeds, either fixed seeds or peer seeds (which are peers remaining in the system after obtaining a complete collection) to stabilize the system. The dominant cause for instability is the missing piece syndrome, whereby one piece becomes very rare in the network. It is shown that stability can be achieved with only a small amount of help from peer seeds--even with very little help from a fixed seed, peers need dwell as peer seeds on average only long enough to upload one additional piece. The region of stability is insensitive to the piece selection policy. Network coding can substantially increase the region of stability in case a portion of the new peers arrive with randomly coded pieces., Comment: 33 pages, 6 figures

Let X be a separable real Banach space having a k-times continuously Fr\'{e}chet differentiable (i.e. C^k-smooth) norm where k=1,...,\infty. We show that any equivalent norm on X can be approximated uniformly on bounded sets by C^k-smooth norms., Comment: 9 pages

We study the problem of selling a resource through an auction mechanism. The winning buyer in turn develops this resource to generate profit. Two forms of payment are considered: charging the winning buyer a one-time payment, or an initial payment plus a profit sharing contract (PSC). We consider a symmetric interdependent values model with risk averse or risk neutral buyers and a risk neutral seller. For the second price auction and the English auction, we show that the seller's expected total revenue from the auction where he also takes a fraction of the positive profit is higher than the expected revenue from the auction with only a one-time payment. Moreover, the seller can generate an even higher expected total revenue if, in addition to taking a fraction of the positive profit, he also takes the same fraction of any loss incurred from developing the resource. Moving beyond simple PSCs, we show that the auction with a PSC from a very general class generates higher expected total revenue than the auction with only a one-time payment. Finally, we show that suitable PSCs provide higher expected total revenue than a one-time payment even when the incentives of the winning buyer to develop the resource must be addressed by the seller., Comment: 36 pages, 2 figure. This is a work in progress

We study efficiency loss in Bayesian revenue optimal auctions. We quantify this as the worst case ratio of loss in the realized social welfare to the social welfare that can be realized by an efficient auction. Our focus is on auctions with single-parameter buyers and where buyers' valuation sets are finite. For binary valued single-parameter buyers with independent (not necessarily identically distributed) private valuations, we show that the worst case efficiency loss ratio (ELR) is no worse than it is with only one buyer; moreover, it is at most 1/2. Moving beyond the case of binary valuations but restricting to single item auctions, where buyers' private valuations are independent and identically distributed, we obtain bounds on the worst case ELR as a function of number of buyers, cardinality of buyers' valuation set, and ratio of maximum to minimum possible values that buyers can have for the item., Comment: 25 pages and 1 figure. A short version of this will appear in the 49th IEEE Conference on Decision and Control (CDC), 2010

We study the problem of characterizing revenue optimal auctions for single-minded buyers. Each buyer is interested only in a specific bundle of items and has a value for the same. Both his bundle and its value are his private information. The bundles that buyers are interested in and their corresponding values are assumed to be realized from known probability distributions independent across the buyers. We identify revenue optimal auctions with a simple structure, if the conditional distribution of any buyer's valuation is nondecreasing, in the hazard rates ordering of probability distributions, as a function of the bundle the buyer is interested in. The revenue optimal auction is given by the solution of a maximum weight independent set problem. We provide a novel graphical construction of the weights and highlight important properties of the resulting auction., Comment: 19 pages, 2 figures. A short version of this will appear in the 49th IEEE Conference on Decision and Control (CDC), 2010

The article introduces a new mechanism for selecting individuals to a Pareto archive. It was combined with a micro-genetic algorithm and tested on several problems. The ability of this approach to produce individuals uniformly distributed along the Pareto set without negative impact on convergence is demonstrated on presented results. The new concept was confronted with NSGA-II, SPEA2, and IBEA algorithms from the PISA package. Another studied effect is the size of population versus number of generations for small populations., Comment: 51 pages, 28 figures

Typical protocols for peer-to-peer file sharing over the Internet divide files to be shared into pieces. New peers strive to obtain a complete collection of pieces from other peers and from a seed. In this paper we investigate a problem that can occur if the seeding rate is not large enough. The problem is that, even if the statistics of the system are symmetric in the pieces, there can be symmetry breaking, with one piece becoming very rare. If peers depart after obtaining a complete collection, they can tend to leave before helping other peers receive the rare piece. Assuming that peers arrive with no pieces, there is a single seed, random peer contacts are made, random useful pieces are downloaded, and peers depart upon receiving the complete file, the system is stable if the seeding rate (in pieces per time unit) is greater than the arrival rate, and is unstable if the seeding rate is less than the arrival rate. The result persists for any piece selection policy that selects from among useful pieces, such as rarest first, and it persists with the use of network coding., Comment: 14 pages, 3 figures in 5 files. An earlier version appeared in the 2010 IEEE International Symposium on Information Theory

We show that if $X$ is an infinite-dimensional separable Banach space (or more generally a Banach space with an infinite-dimensional separable quotient) then there is a continuous mapping $f\colon X\to X$ such that the autonomous differential equation $x'=f(x)$ has no solution at any point.

A tight upper bound is given on the distribution of the maximum of a supermartingale. Specifically, it is shown that if $Y$ is a semimartingale with initial value zero and quadratic variation process $[Y,Y]$ such that $Y + [Y,Y]$ is a supermartingale, then the probability the maximum of $Y$ is greater than or equal to a positive constant $a$ is less than or equal to $1/(1+a).$ The proof makes use of the semimartingale calculus and is inspired by dynamic programming., Comment: 13 pages, no figures

The increasing utilization of charged particle beams for therapeutic purposes requires designing novel detector systems which shall be capable of assessing radiation quality for a diversity of ion species. It is shown that the pattern of energy deposition in thermoluminescent phosphors and biological tissue contains conceptual parallels. The correlation of physical and radiobiological parameters observed experimentally for specific endpoints (single- and double-strand breaks of DNA) opens the possibility of realizing successfully quasi-biological solid-state nanodosimetry on the basis of thermoluminescence., Comment: 4 pages, 1 figure

We show that if an infinite-dimensional Banach space X has a symmetric basis then there exists a bounded, linear operator R : X --> X such that the set A = {x in X : ||R^n(x)|| --> infinity} is non-empty and nowhere dense in X. Moreover, if x in X\A then some subsequence of (R^n(x)) converges weakly to x. This answers in the negative a recent conjecture of Prajitura. The result can be extended to any Banach space containing an infinite-dimensional, complemented subspace with a symmetric basis; in particular, all 'classical' Banach spaces admit such an operator.