In the present day, more than 3.8 billion people around the world actively use social media. The effectiveness of social media in facilitating quick and easy sharing of information has attracted brands and advertizers who wish to use the platform to
market products via the influencers in the network. Influencers, owing to their massive popularity, provide a huge potential customer base generating higher returns of investment in a very short period. However, it is not straightforward to decide which influencers should be selected for an advertizing campaign that can generate maximum returns with minimum investment. In this work, we present an agent-based model (ABM) that can simulate the dynamics of influencer advertizing campaigns in a variety of scenarios and can help to discover the best influencer marketing strategy. Our system is a probabilistic graph-based model that incorporates real-world factors such as customers interest in a product, customer behavior, the willingness to pay, a brands investment cap, influencers engagement with influence diffusion, and the nature of the product being advertized viz. luxury and non-luxury.
Neuromorphic computing describes the use of VLSI systems to mimic neuro-biological architectures and is also looked at as a promising alternative to the traditional von Neumann architecture. Any new computing architecture would need a system that can
perform floating-point arithmetic. In this paper, we describe a neuromorphic system that performs IEEE 754-compliant floating-point multiplication. The complex process of multiplication is divided into smaller sub-tasks performed by components Exponent Adder, Bias Subtractor, Mantissa Multiplier and Sign OF/UF. We study the effect of the number of neurons per bit on accuracy and bit error rate, and estimate the optimal number of neurons needed for each component.
Modeling social interactions based on individual behavior has always been an area of interest, but prior literature generally presumes rational behavior. Thus, such models may miss out on capturing the effects of biases humans are susceptible to. Thi
s work presents a method to model egocentric bias, the real-life tendency to emphasize ones own opinion heavily when presented with multiple opinions. We use a symmetric distribution centered at an agents own opinion, as opposed to the Bounded Confidence (BC) model used in prior work. We consider a game of iterated interactions where an agent cooperates based on its opinion about an opponent. Our model also includes the concept of domain-based self-doubt, which varies as the interaction succeeds or not. An increase in doubt makes an agent reduce its egocentricity in subsequent interactions, thus enabling the agent to learn reactively. The agent system is modeled with factions not having a single leader, to overcome some of the issues associated with leader-follower factions. We find that agents belonging to factions perform better than individual agents. We observe that an intermediate level of egocentricity helps the agent perform at its best, which concurs with conventional wisdom that neither overconfidence nor low self-esteem brings benefits.
We present a new $4$-approximation algorithm for the Combinatorial Motion Planning problem which runs in $mathcal{O}(n^2alpha(n^2,n))$ time, where $alpha$ is the functional inverse of the Ackermann function, and a fully distributed version for the sa
me in asynchronous message passing systems, which runs in $mathcal{O}(nlog_2n)$ time with a message complexity of $mathcal{O}(n^2)$. This also includes the first fully distributed algorithm in asynchronous message passing systems to perform shortcut operations on paths, a procedure which is important in approximation algorithms for the vehicle routing problem and its variants. We also show that our algorithm gives feasible solutions to the $k$-TSP problem with an approximation factor of $2$ in both centralized and distributed environments. The broad idea of the algorithm is to distribute the set of vertices into two subsets and construct paths for each salesman over each of the two subsets. Finally we combine these pairwise disjoint paths for each salesman to obtain a set of paths that span the entire graph. This is similar to the algorithm by Yadlapalli et. al. cite{3.66} but differs in respect to the fact that it does not require us to use minimum cost matching as a subroutine, and hence can be easily distributed.
We consider the distributed version of the Multiple Knapsack Problem (MKP), where $m$ items are to be distributed amongst $n$ processors, each with a knapsack. We propose different distributed approximation algorithms with a tradeoff between time and
message complexities. The algorithms are based on the greedy approach of assigning the best item to the knapsack with the largest capacity. These algorithms obtain a solution with a bound of $frac{1}{n+1}$ times the optimum solution, with either $mathcal{O}left(mlog nright)$ time and $mathcal{O}left(m nright)$ messages, or $mathcal{O}left(mright)$ time and $mathcal{O}left(mn^{2}right)$ messages.
This paper defines a distance function that measures the dissimilarity between planar geometric figures formed with straight lines. This function can in turn be used in partial matching of different geometric figures. For a given pair of geometric fi
gures that are graphically isomorphic, one function measures the angular dissimilarity and another function measures the edge length disproportionality. The distance function is then defined as the convex sum of these two functions. The novelty of the presented function is that it satisfies all properties of a distance function and the computation of the same is done by projecting appropriate features to a cartesian plane. To compute the deviation from the angular similarity property, the Euclidean distance between the given angular pairs and the corresponding points on the $y=x$ line is measured. Further while computing the deviation from the edge length proportionality property, the best fit line, for the set of edge lengths, which passes through the origin is found, and the Euclidean distance between the given edge length pairs and the corresponding point on a $y=mx$ line is calculated. Iterative Proportional Fitting Procedure (IPFP) is used to find this best fit line. We demonstrate the behavior of the defined function for some sample pairs of figures.
Given a system model where machines have distinct speeds and power ratings but are otherwise compatible, we consider various problems of scheduling under resource constraints on the system which place the restriction that not all machines can be run
at once. These can be power, energy, or makespan constraints on the system. Given such constraints, there are problems with divisible as well as non-divisible jobs. In the setting where there is a constraint on power, we show that the problem of minimizing makespan for a set of divisible jobs is NP-hard by reduction to the knapsack problem. We then show that scheduling to minimize energy with power constraints is also NP-hard. We then consider scheduling with energy and makespan constraints with divisible jobs and show that these can be solved in polynomial time, and the problems with non-divisible jobs are NP-hard. We give exact and approximation algorithms for these problems as required.
The problem of attaining energy efficiency in distributed systems is of importance, but a general, non-domain-specific theory of energy-minimal scheduling is far from developed. In this paper, we classify the problems of energy-minimal scheduling and
present theoretical foundations of the same. We derive results concerning energy-minimal scheduling of independent jobs in a distributed system with functionally similar machines with different working and idle power ratings. The machines considered in our system can have identical as well as different speeds. If the jobs can be divided into arbitrary parts, we show that the minimum-energy schedule can be generated in linear time and give exact scheduling algorithms. For the cases where jobs are non-divisible, we prove that the scheduling problems are NP-hard and also give approximation algorithms for the same along with their bounds.
The relationship between Heyting algebras (HA) and semirings is explored. A new class of HAs called Symmetric Heyting algebras (SHAs) is proposed, and a necessary condition on SHAs to be consider semirings is given. We define a new mathematical famil
y called Heyting structures, which are similar to semirings, but with Heyting-algebra operators in place of the usual arithmetic operators usually seen in semirings. The impact of the zero-sum free property of semirings on Heyting structures is shown as also the condition under which it is possible to extend one Heyting structure to another. It is also shown that the union of two or more sets forming Heyting structures is again a Heyting structure, if the operators on the new structure are suitably derived from those of the component structures. The analysis also provides a sufficient condition such that the larger Heyting structure satisfying a monotony law implies that the ones forming the union do so as well.
We define a emph{thermal network}, which is a network where the flow functionality of a node depends upon its temperature. This model is inspired by several types of real-life networks, and generalizes some conventional network models wherein nodes h
ave fixed capacities and the problem is to maximize the flow through the network. In a thermal network, the temperature of a node increases as traffic moves through it, and nodes may also cool spontaneously over time, or by employing cooling packets. We analyze the problems of maximizing the flow from a source to a sink for both these cases, for a holistic view with respect to the single-source-single-sink dynamic flow problem in a thermal network. We have studied certain properties such a thermal network exhibits, and give closed-form solutions for the maximum flow that can be achieved through such a network.
