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We give an axiomatic foundation to $\Lambda$-quantiles, a family of generalized quantiles introduced by Frittelli et al. (2014) under the name of Lambda Value at Risk. Under mild assumptions, we show that these functionals are characterized by a property that we call "locality", that means that any change in the distribution of the probability mass that arises entirely above or below the value of the $\Lambda$-quantile does not modify its value. We compare with a related axiomatization of the usual quantiles given by Chambers (2009), based on the stronger property of "ordinal covariance", that means that quantiles are covariant with respect to increasing transformations. Further, we present a systematic treatment of the properties of $\Lambda$-quantiles, refining some of the results of Frittelli et al. (2014) and Burzoni et al. (2017) and showing that in the case of a nonincreasing $\Lambda$ the properties of $\Lambda$-quantiles closely resemble those of the usual quantiles.

We consider a participatory budgeting problem in which each voter submits a proposal for how to divide a single divisible resource (such as money or time) among several possible alternatives (such as public projects or activities) and these proposals must be aggregated into a single aggregate division. Under $\ell_1$ preferences -- for which a voter's disutility is given by the $\ell_1$ distance between the aggregate division and the division he or she most prefers -- the social welfare-maximizing mechanism, which minimizes the average $\ell_1$ distance between the outcome and each voter's proposal, is incentive compatible (Goel et al. 2016). However, it fails to satisfy the natural fairness notion of proportionality, placing too much weight on majority preferences. Leveraging a connection between market prices and the generalized median rules of Moulin (1980), we introduce the independent markets mechanism, which is both incentive compatible and proportional. We unify the social welfare-maximizing mechanism and the independent markets mechanism by defining a broad class of moving phantom mechanisms that includes both. We show that every moving phantom mechanism is incentive compatible. Finally, we characterize the social welfare-maximizing mechanism as the unique Pareto-optimal mechanism in this class, suggesting an inherent tradeoff between Pareto optimality and proportionality.

We establish a complete classification of binary group codes with complementary duals for a finite group and explicitly determine the number of linear complementary dual (LCD) cyclic group codes by using cyclotomic cosets. The dimension and the minimum distance for LCD group codes are explored. Finally, we find a connection between LCD MDS group codes and maximal ideals.

Beyond Visual Line of Sight operation enables drones to surpass the limits imposed by the reach and constraints of their operator's eyes. It extends their range and, as such, productivity, and profitability. Drones operating BVLOS include a variety of highly sensitive assets and information that could be subject to unintentional or intentional security vulnerabilities. As a solution, blockchain-based services could enable secure and trustworthy exchange and storage of related data. They also allow for traceability of exchanges and perform synchronization with other nodes in the network. However, most of the blockchain-based approaches focus on the network and the protocol aspects of drone systems. Few studies focus on the architectural level of on-chip compute platforms of drones. Based on this observation, the contribution of this paper is twofold: (1) a generic blockchain-based service architecture for on-chip compute platforms of drones, and (2) a concrete example realization of the proposed generic architecture.

For distributed protocols involving many servers, assuming that they do not collude with each other makes some secrecy problems solvable and reduces overheads and computational hardness assumptions in others. While the non-collusion assumption is pervasive among privacy-preserving systems, it remains highly susceptible to covert, undetectable collusion among computing parties. This work stems from an observation that if the number of available computing parties is much higher than the number of parties required to perform a secure computation, collusion attempts could be deterred. We focus on the standard problem of multi-server private information retrieval (PIR) that inherently assumes that servers do not collude. For PIR application scenarios, such as those for blockchain light clients, where the available servers are plentiful, a single server's deviating action is not tremendously beneficial to itself. We can make deviations undesired through small amounts of rewards and penalties, thus raising the bar for collusion significantly. For any given multi-server 1-private PIR (i.e. the base PIR scheme is constructed assuming no pairwise collusion), we provide a collusion mitigation mechanism. We first define a two-stage sequential game that captures how rational servers interact with each other during collusion, then determine the payment rules such that the game realizes the unique sequential equilibrium: a non-collusion outcome. We also offer privacy protection for an extended period beyond the time the query executions happen, and guarantee user compensation in case of a reported privacy breach. Overall, we conjecture that the incentive structure for collusion mitigation to be functional towards relaxing the strong non-collusion assumptions across a variety of multi-party computation tasks.

A \emph{general branch-and-bound tree} is a branch-and-bound tree which is allowed to use general disjunctions of the form $\pi^{\top} x \leq \pi_0 \,\vee\, \pi^{\top}x \geq \pi_0 + 1$, where $\pi$ is an integer vector and $\pi_0$ is an integer scalar, to create child nodes. We construct a packing instance, a set covering instance, and a Traveling Salesman Problem instance, such that any general branch-and-bound tree that solves these instances must be of exponential size. We also verify that an exponential lower bound on the size of general branch-and-bound trees persists when we add Gaussian noise to the coefficients of the cross polytope, thus showing that polynomial-size "smoothed analysis" upper bound is not possible. The results in this paper can be viewed as the branch-and-bound analog of the seminal paper by Chv\'atal et al. \cite{chvatal1989cutting}, who proved lower bounds for the Chv\'atal-Gomory rank.

The undecidability of basic decision problems for general FIFO machines such as reachability and unboundedness is well-known. In this paper, we provide an underapproximation for the general model by considering only runs that are input-bounded (i.e. the sequence of messages sent through a particular channel belongs to a given bounded language). We prove, by reducing this model to a counter machine with restricted zero tests, that the rational-reachability problem (and by extension, control-state reachability, unboundedness, deadlock, etc.) is decidable. This class of machines subsumes input-letter-bounded machines, flat machines, linear FIFO nets, and monogeneous machines, for which some of these problems were already shown to be decidable. These theoretical results can form the foundations to build a tool to verify general FIFO machines based on the analysis of input-bounded machines.

We show that there exists no algorithm that decides for any bilinear system $(B,v)$ if the growth rate of $(B,v)$ is $1$. This answers a question of Bui who showed that if the coefficients are positive the growth rate is computable (i.e., there is an algorithm that outputs the sequence of digits of the growth rate of $(B,v)$). Our proof is based on a reduction of the computation of the joint spectral radius of a set of matrices to the computation of the growth rate of a bilinear system. We also use our reduction to deduce that there exists no algorithm that approximates the growth rate of a bilinear system with relative accuracy $\varepsilon$ in time polynomial in the size of the system and of $\varepsilon$. Our two results hold even if all the coefficients are nonnegative rationals.

In this paper, based on results of exact learning, test theory, and rough set theory, we study arbitrary infinite families of concepts each of which consists of an infinite set of elements and an infinite set of subsets of this set called concepts. We consider the notion of a problem over a family of concepts that is described by a finite number of elements: for a given concept, we should recognize which of the elements under consideration belong to this concept. As algorithms for problem solving, we consider decision trees of five types: (i) using membership queries, (ii) using equivalence queries, (iii) using both membership and equivalence queries, (iv) using proper equivalence queries, and (v) using both membership and proper equivalence queries. As time complexity, we study the depth of decision trees. In the worst case, with the growth of the number of elements in the problem description, the minimum depth of decision trees of the first type either grows as a logarithm or linearly, and the minimum depth of decision trees of each of the other types either is bounded from above by a constant or grows as a logarithm, or linearly. The obtained results allow us to distinguish seven complexity classes of infinite families of concepts.

This project addresses the problem of sentiment analysis in twitter; that is classifying tweets according to the sentiment expressed in them: positive, negative or neutral. Twitter is an online micro-blogging and social-networking platform which allows users to write short status updates of maximum length 140 characters. It is a rapidly expanding service with over 200 million registered users - out of which 100 million are active users and half of them log on twitter on a daily basis - generating nearly 250 million tweets per day. Due to this large amount of usage we hope to achieve a reflection of public sentiment by analysing the sentiments expressed in the tweets. Analysing the public sentiment is important for many applications such as firms trying to find out the response of their products in the market, predicting political elections and predicting socioeconomic phenomena like stock exchange. The aim of this project is to develop a functional classifier for accurate and automatic sentiment classification of an unknown tweet stream.