Approximation Algorithms for Envy-Free Cake Division with Connected Pieces

Cake cutting is a classic model for studying fair division of a heterogeneous, divisible resource among agents with individual preferences. Addressing cake division under a typical requirement that each agent must receive a connected piece of the cake, we develop approximation algorithms for finding envy-free (fair) cake divisions. In particular, this work improves the state-of-the-art additive approximation bound for this fundamental problem. Our results hold for general cake division instances in which the agents\u27 valuations satisfy basic assumptions and are normalized (to have value 1 for the cake). Furthermore, the developed algorithms execute in polynomial time under the standard Robertson-Webb query model. Prior work has shown that one can efficiently compute a cake division (with connected pieces) in which the additive envy of any agent is at most 1/3. An efficient algorithm is also known for finding connected cake divisions that are (almost) 1/2-multiplicatively envy-free. Improving the additive approximation guarantee and maintaining the multiplicative one, we develop a polynomial-time algorithm that computes a connected cake division that is both (1/4 +o(1))-additively envy-free and (1/2 - o(1))-multiplicatively envy-free. Our algorithm is based on the ideas of interval growing and envy-cycle elimination. In addition, we study cake division instances in which the number of distinct valuations across the agents is parametrically bounded. We show that such cake division instances admit a fully polynomial-time approximation scheme for connected envy-free cake division

On Fair and Efficient Allocations of Indivisible Public Goods

We study fair allocation of indivisible public goods subject to cardinality (budget) constraints. In this model, we have n agents and m available public goods, and we want to select k ? m goods in a fair and efficient manner. We first establish fundamental connections between the models of private goods, public goods, and public decision making by presenting polynomial-time reductions for the popular solution concepts of maximum Nash welfare (MNW) and leximin. These mechanisms are known to provide remarkable fairness and efficiency guarantees in private goods and public decision making settings. We show that they retain these desirable properties even in the public goods case. We prove that MNW allocations provide fairness guarantees of Proportionality up to one good (Prop1), 1/n approximation to Round Robin Share (RRS), and the efficiency guarantee of Pareto Optimality (PO). Further, we show that the problems of finding MNW or leximin-optimal allocations are NP-hard, even in the case of constantly many agents, or binary valuations. This is in sharp contrast to the private goods setting that admits polynomial-time algorithms under binary valuations. We also design pseudo-polynomial time algorithms for computing an exact MNW or leximin-optimal allocation for the cases of (i) constantly many agents, and (ii) constantly many goods with additive valuations. We also present an O(n)-factor approximation algorithm for MNW which also satisfies RRS, Prop1, and 1/2-Prop

Electronic Fund Transfer: A study of security control in selected banks of Pune Region

In Current Era all the banks are running along with the technology almost all the banks provides electronic find transfer either through cell phone or through computer system or through any other electronic device. There is need of software for performing such kind of transaction as well as enrolment of third party tool. Now a days ATM as well as other handhold devices like cell phone evolve in such transaction. All the banks working. While increasing technological impact in other hand barriers as well as theft in electronic transaction increases. Such as hacking, gaining access of cards, online fraud etc. The security while transferring fund is an important concern all the banks trying to increase security in online transaction. For the same they use several technological tools. This paper will discuss importance of security as well as measures taken care while implementing security in fund transfer

Sublinear Approximation Algorithm for Nash Social Welfare with XOS Valuations

We study the problem of allocating indivisible goods among $n$ agents with the objective of maximizing Nash social welfare (NSW). This welfare function is defined as the geometric mean of the agents' valuations and, hence, it strikes a balance between the extremes of social welfare (arithmetic mean) and egalitarian welfare (max-min value). Nash social welfare has been extensively studied in recent years for various valuation classes. In particular, a notable negative result is known when the agents' valuations are complement-free and are specified via value queries: for XOS valuations, one necessarily requires exponentially many value queries to find any sublinear (in $n$) approximation for NSW. Indeed, this lower bound implies that stronger query models are needed for finding better approximations. Towards this, we utilize demand oracles and XOS oracles; both of these query models are standard and have been used in prior work on social welfare maximization with XOS valuations. We develop the first sublinear approximation algorithm for maximizing Nash social welfare under XOS valuations, specified via demand and XOS oracles. Hence, this work breaks the $O(n)$-approximation barrier for NSW maximization under XOS valuations. We obtain this result by developing a novel connection between NSW and social welfare under a capped version of the agents' valuations. In addition to this insight, which might be of independent interest, this work relies on an intricate combination of multiple technical ideas, including the use of repeated matchings and the discrete moving knife method. In addition, we partially complement the algorithmic result by showing that, under XOS valuations, an exponential number of demand and XOS queries are necessarily required to approximate NSW within a factor of $\left(1 - \frac{1}{e}\right)$.Comment: 41 page

Neuroregenerative-Rehabilitative Therapy for Spinal Cord Injury

Spinal cord injury is one of the leading causes of disability worldwide. Current mainstay treatment strategies consist of surgical and medical management in acute and subacute stage. Rehabilitative management in the chronic stage. None of the existing strategies can repair the damage to the spinal cord and recover neurological functioning. Stem cells have promising results in pre-clinical and clinical studies. Various pre-clinical studies have evidenced neuro-regenerative capabilities of stem cells and shown neural recovery. Clinical studies have also shown improvements in neurological functions and quality of life. This chapter discusses about different types of cells available, routes of administration available to transplant these cells, dosages of cell and optimum time after injury at which cells should be transplanted based on world-wide literature. We have also discussed results following our protocol of intrathecal transplantation of autologous bone marrow mononuclear cells. Although, not a cure, stem cell therapy further improves quality of life, functional independence and reduces secondary complications when combined with existing treatment strategies; neuroregenerative rehabilitative therapy

A Comparative Analysis of Frontal, Maxillary Sinus and Pyriform Aperture as Gender Identification Tool Using Radiographic Morphometric Parameters

The study was done with the aim to check for the reliability of morphometric parameters of frontal and maxillary sinuses along with pyriform aperture for sexual dimorphism on posteroanterior skull radiograph in young adults. 30 individuals with equal distribution of females and males were selected considering inclusion and exclusion criteria and PA skull view of same were analyzed for frontal sinus, maxillary sinus and pyriform aperture parameters using Carestream Dental imaging software 6.14.7 CS 3D. Statistical analysis establishes frontal and maxillary sinus parameters in comparison to pyriform aperture parameters as reliable tool for gender assessment