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An efficient caching can be achieved by predicting the popularity of the files accurately. It is well known that the popularity of a file can be nudged by using recommendation, and hence it can be estimated accurately leading to an efficient caching strategy. Motivated by this, in this paper, we consider the problem of joint caching and recommendation in a 5G and beyond heterogeneous network. We model the influence of recommendation on demands by a Probability Transition Matrix (PTM). The proposed framework consists of estimating the PTM and use them to jointly recommend and cache the files. In particular, this paper considers two estimation methods namely a) Bayesian estimation and b) a genie aided Point estimation. An approximate high probability bound on the regret of both the estimation methods are provided. Using this result, we show that the approximate regret achieved by the genie aided Point estimation approach is $\mathcal{O}(T^{2/3} \sqrt{\log T})$ while the Bayesian estimation method achieves a much better scaling of $\mathcal{O}(\sqrt{T})$. These results are extended to a heterogeneous network consisting of M small base stations (sBSs) with a central macro base station. The estimates are available at multiple sBSs, and are combined using appropriate weights. Insights on the choice of these weights are provided by using the derived approximate regret bound in the multiple sBS case. Finally, simulation results confirm the superiority of the proposed algorithms in terms of average cache hit rate, delay and throughput., 34 pages, 6 figures

Federated Learning (FL) has evolved as a promising technique to handle distributed machine learning across edge devices. A single neural network (NN) that optimises a global objective is generally learned in most work in FL, which could be suboptimal for edge devices. Although works finding a NN personalised for edge device specific tasks exist, they lack generalisation and/or convergence guarantees. In this paper, a novel communication efficient FL algorithm for personalised learning in a wireless setting with guarantees is presented. The algorithm relies on finding a ``better`` empirical estimate of losses at each device, using a weighted average of the losses across different devices. It is devised from a Probably Approximately Correct (PAC) bound on the true loss in terms of the proposed empirical loss and is bounded by (i) the Rademacher complexity, (ii) the discrepancy, (iii) and a penalty term. Using a signed gradient feedback to find a personalised NN at each device, it is also proven to converge in a Rayleigh flat fading (in the uplink) channel, at a rate of the order max{1/SNR,1/sqrt(T)} Experimental results show that the proposed algorithm outperforms locally trained devices as well as the conventionally used FedAvg and FedSGD algorithms under practical SNR regimes.

Design of distributed caching mechanisms is considered as an active area of research due to its promising solution in reducing data load in the backhaul link of a cellular network. In this paper, the problem of distributed content caching in a small-cell Base Stations (sBSs) wireless network that maximizes the cache hit performance is considered. Most of the existing works focus on static demands, however, here, data at each sBS is considered to be correlated across time and sBSs. The caching strategy is assumed to be a weighted combination of past caching strategies. A high probability generalization guarantees on the performance of the proposed caching strategy is derived. The theoretical guarantee provides following insights on obtaining the caching strategy: (i) run regret minimization at each sBS to obtain a sequence of caching strategies across time, and (ii) maximize an estimate of the bound to obtain a set of weights for the caching strategy which depends on the discrepancy. Also, theoretical guarantee on the performance of the LRFU caching strategy is derived. Further, federated learning based heuristic caching algorithm is also proposed. Finally, it is shown through simulations using Movie Lens dataset that the proposed algorithm significantly outperforms LRFU algorithm., 30 pages, 6 figures

We consider a wireless ad hoc network in the presence of eavesdroppers (EDs), where the nodes are distributed according to independent Poisson point processes (PPPs). The legitimate nodes follow the half-duplex mode of operation employing the slotted ALOHA protocol for transmission. For such a network, a novel communication scheme that induces a time-varying secure connectivity graph (SCG) is proposed, and the connectivity behavior of this induced SCG is studied. In particular, for a legitimate node in the network, we analyze (i) the average number of incoming edges and the average number of outgoing edges; (ii) the time to nearest-neighbor secure connectivity; and (iii) a condition on the EDs' density that allows information percolation, {\ie}, a condition for the existence of a `giant' component. The average time for secure connectivity among the nodes in this giant component is shown to scale linearly with the Euclidean distance. Further, we show that by splitting the packets into two sub-packets and routing each sub-packet along paths that are sufficiently far apart can (a) potentially improve secure connectivity and (b) reduce the overall delay incurred in exchanging packets between any two legitimate nodes in the giant component., An abridged version of this paper was submitted to IEEE GLOBECOM 2019

In this paper, we consider a distributed stochastic optimization problem where the goal is to minimize the time average of a cost function subject to a set of constraints on the time averages of related stochastic processes called penalties. We assume that the state of the system is evolving in an independent and non-stationary fashion and the "common information" available at each node is distributed and delayed. Such stochastic optimization is an integral part of many important problems in wireless networks such as scheduling, routing, resource allocation and crowd sensing. We propose an approximate distributed Drift- Plus-Penalty (DPP) algorithm, and show that it achieves a time average cost (and penalties) that is within epsilon > 0 of the optimal cost (and constraints) with high probability. Also, we provide a condition on the convergence time t for this result to hold. In particular, for any delay D >= 0 in the common information, we use a coupling argument to prove that the proposed algorithm converges almost surely to the optimal solution. We use an application from wireless sensor network to corroborate our theoretical findings through simulation results., 16 pages + 5 figures

This paper considers a distributed stochastic optimization problem where the goal is to minimize the time average of a cost function subject to a set of constraints on the time averages of a related stochastic processes called penalties. We assume that a delayed information about an event in the system is available as a common information at every user, and the state of the system is evolving in an independent and non-stationary fashion. We show that an approximate Drift-plus-penalty (DPP) algorithm that we propose achieves a time average cost that is within some positive constant epsilon of the optimal cost with high probability. Further, we provide a condition on the waiting time for this result to hold. The condition is shown to be a function of the mixing coefficient, the number of samples (w) used to compute an estimate of the distribution of the state, and the delay. Unlike the existing work, the method used in the paper can be adapted to prove high probability results when the state is evolving in a non-i.i.d and non-stationary fashion. Under mild conditions, we show that the dependency of the error bound on w is exponential, which is a significant improvement compared to the exiting work., A part of this work is submitted to WCNC-2017

BACKGROUND: Anterior cruciate ligament is an intra - articular, extra synovial structure present in the central complex of knee joint. It functions in concert with all ot her anatomical structures in the knee joint to control and limit motion and to maintain both static and dynamic equilibrium. It is commonly injured in athletic activities specially contact sports and motor vehicle accidents. Ligament disruption occurs with out a fall or direct contact where deceleration along with valgus external rotation or hyper extension force comes into play. T h e a im o f s u r g ical tre a tme n t is to rest o r e k n e e st ab i l it y , t he re b y a l l o w ing t h e pa ti e n t to return to h is o r ig in a l ph y sical a ct i v i t y l e v e ls. T h e c h o ice o f g r a f t a n d its f i x a ti o n p la y s a k e y role in ACL re c on st r u cti o n. A n id ea l g ra f t w ou ld b e o n e t h a t p ro v id e s a s m u ch stre n g th a s n a ti v e an t e r i o r c r u cia t e l ig am e n t, a l l o w s f o r s e c u re f i x a t i on , h a s m inimal ha r v e st site mo rbidit y , e n a b les u n restr i ct e d re h ab i l it a t i o n a n d rest o res no r ma l k n e e b iomec h a n ics a n d ki ne ma tics. A I M : T o a s s e ss t h e e f fe ct iv ene ss o f t h e bo n e - p a t e l l a r t e n do n - b on e g raft c om p a red to ha m str i n g t endo n g r a f t a s u s e d in t h e tr e a t me n t o f an t e r i o r c r u ci a te li g a m en t in j u r i e s o f t h e k n ee . DESIGN : This is a prospective study. MATERIALS AND METHODS : This prospective study was conducted at a tertiary hospital for a pe r io d o f t w e l v e m on t h s f rom June 2013 t o July 2 014 . Patients presenting with unilateral knee injury in Outpatient depa rtment and Casualty of the hospital were evaluated by a thorough general and local clinical examination of the knee. Uninjured knees of same subjects in supine position were taken as reference. Subjects fulfilling the predetermined inclusion and exclusion criteria were included in the study. STATISTICAL METHODS : Intergroup comparison was analysed by K - Independent sample t test. Intragroup comparison was analysed by Paired t - test. RESULTS : Patients were divided into two groups and treated with using Bone - patellar tendon - bone graft and Hamstring graft respectively. Mean age group of patients was 29.16 yrs. (range 16 - 51yrs) and 30.88 yrs. (range 19 - 48yrs) in group A and B respectively we found the incidence of ACL injury in 15 - 44 years age group to be greater than twice the general population. A mean delay in surgery of 4.66 months (range 2 - 12 months) since the time of injury in group A and 4.46 months (range 2 - 7 months) in group B was observed. Subjective IKDC evaluation was done at the end of 12 months. Ther e was no difference in both the groups in the terms of effusion, passive motion, knee compartment findings, ligament examination, X - ray findings. Functional test and IKDC grade of both the groups showed statistically very highly significant improvement. Ho wever, there was statistically very high Harvest site pathology in group A. CONCLUSION : We found that there is statistically no significant difference in the overall clinical outcome between hamstring autograft with transfix and bone - patellar tendon bone autograft with interference screw except that the patellar tendon group had a greater tendency of having donor site morbidity compared to the hamstring tendon group.

A heterogenous network is considered where the base stations (BSs), small base stations (SBSs) and users are distributed according to independent Poisson point processes (PPPs). We let the SBS nodes to posses high storage capacity and are assumed to form a distributed caching network. Popular data files are stored in the local cache of SBS, so that users can download the desired files from one of the SBS in the vicinity subject to availability. The offloading-loss is captured via a cost function that depends on a random caching strategy proposed in this paper. The cost function depends on the popularity profile, which is, in general, unknown. In this work, the popularity profile is estimated at the BS using the available instantaneous demands from the users in a time interval $[0,\tau]$. This is then used to find an estimate of the cost function from which the optimal random caching strategy is devised. The main results of this work are the following: First it is shown that the waiting time $\tau$ to achieve an $\epsilon>0$ difference between the achieved and optimal costs is finite, provided the user density is greater than a predefined threshold. In this case, $\tau$ is shown to scale as $N^2$, where $N$ is the support of the popularity profile. Secondly, a transfer learning-based approach is proposed to obtain an estimate of the popularity profile used to compute the empirical cost function. A condition is derived under which the proposed transfer learning-based approach performs better than the random caching strategy., Comment: 6 pages, Proceedings of IEEE Global Communications Conference, 2015