Generalized Interlinked Cycle Cover for Index Coding

A source coding problem over a noiseless broadcast channel where the source is pre-informed about the contents of the cache of all receivers, is an index coding problem. Furthermore, if each message is requested by one receiver, then we call this an index coding problem with a unicast message setting. This problem can be represented by a directed graph. In this paper, we first define a structure (we call generalized interlinked cycles (GIC)) in directed graphs. A GIC consists of cycles which are interlinked in some manner (i.e., not disjoint), and it turns out that the GIC is a generalization of cliques and cycles. We then propose a simple scalar linear encoding scheme with linear time encoding complexity. This scheme exploits GICs in the digraph. We prove that our scheme is optimal for a class of digraphs with message packets of any length. Moreover, we show that our scheme can outperform existing techniques, e.g., partial clique cover, local chromatic number, composite-coding, and interlinked cycle cover.Comment: Extended version of the paper which is to be presented at the IEEE Information Theory Workshop (ITW), 2015 Jej

Graph-Theoretic Approaches to Two-Sender Index Coding

Consider a communication scenario over a noiseless channel where a sender is required to broadcast messages to multiple receivers, each having side information about some messages. In this scenario, the sender can leverage the receivers' side information during the encoding of messages in order to reduce the required transmissions. This type of encoding is called index coding. In this paper, we study index coding with two cooperative senders, each with some subset of messages, and multiple receivers, each requesting one unique message. The index coding in this setup is called two-sender unicast index coding (TSUIC). The main aim of TSUIC is to minimize the total number of transmissions required by the two senders. Based on graph-theoretic approaches, we prove that TSUIC is equivalent to single-sender unicast index coding (SSUIC) for some special cases. Moreover, we extend the existing schemes for SSUIC, viz., the cycle-cover scheme, the clique-cover scheme, and the local-chromatic scheme to the corresponding schemes for TSUIC.Comment: To be presented at 2016 IEEE Global Communications Conference (GLOBECOM 2016) Workshop on Network Coding and Applications (NetCod), Washington, USA, 201

Nonadiabatic quantum transition-state theory in the golden-rule limit. I. Theory and application to model systems

We propose a new quantum transition-state theory for calculating Fermi's golden-rule rates in complex multidimensional systems. This method is able to account for the nuclear quantum effects of delocalization, zero-point energy and tunnelling in an electron-transfer reaction. It is related to instanton theory but can be computed by path-integral sampling and is thus applicable to treat molecular reactions in solution. A constraint functional based on energy conservation is introduced which ensures that the dominant paths contributing to the reaction rate are sampled. We prove that the theory gives exact results for a system of crossed linear potentials and also the correct classical limit for any system. In numerical tests, the new method is also seen to be accurate for anharmonic systems, and even gives good predictions for rates in the Marcus inverted regime.Comment: 18 pages and 6 figure

WKB Approximation to the Power Wall

We present a semiclassical analysis of the quantum propagator of a particle confined on one side by a steeply, monotonically rising potential. The models studied in detail have potentials proportional to $x^{\alpha}$ for $x>0$; the limit $\alpha\to\infty$ would reproduce a perfectly reflecting boundary, but at present we concentrate on the cases $\alpha =1$ and 2, for which exact solutions in terms of well known functions are available for comparison. We classify the classical paths in this system by their qualitative nature and calculate the contributions of the various classes to the leading-order semiclassical approximation: For each classical path we find the action $S$, the amplitude function $A$ and the Laplacian of $A$. (The Laplacian is of interest because it gives an estimate of the error in the approximation and is needed for computing higher-order approximations.) The resulting semiclassical propagator can be used to rewrite the exact problem as a Volterra integral equation, whose formal solution by iteration (Neumann series) is a semiclassical, not perturbative, expansion. We thereby test, in the context of a concrete problem, the validity of the two technical hypotheses in a previous proof of the convergence of such a Neumann series in the more abstract setting of an arbitrary smooth potential. Not surprisingly, we find that the hypotheses are violated when caustics develop in the classical dynamics; this opens up the interesting future project of extending the methods to momentum space.Comment: 30 pages, 8 figures. Minor corrections in v.

Understanding security risks and users perception towards adopting wearable Internet of Medical Things

This thesis examines users’ perception of trust within the context of security and privacy of Wearable Internet of Medical Things (WIoMT). WIoMT is a collective term for all medical devices connected to internet to facilitate collection and sharing of health-related data such as blood pressure, heart rate, oxygen level and more. Common wearable devices include smart watches and fitness bands. WIoMT, a phenomenon due to Internet of Things (IoT) has become prevalent in managing the day-to-day activities and health of individuals. This increased growth and adoption poses severe security and privacy concerns. Similar to IoT, there is a need to analyse WIoMT security risks as they are used by individuals and organisations on regular basis, risking personal and confidential information. Additionally, for better implementation, performance, adoption, and secured wearable medical devices, it is crucial to observe users’ perception. Users’ perspectives towards trust are critical for adopting WIoMT. This research aimed to understand users’ perception of trust in the adoption of WIoMT, while also exploring the security risks associated with adopting wearable IoMT. Employing a quantitative method approach, 189 participants from Western Sydney University completed an online survey. The results of the study and research model indicated more than half of the variance (R2 = 0.553) in the Intention to Use WIoMT devices, which was determined by the significant predictors (95% Confidence Interval; p < 0.05), Perceived Usefulness, Perceived Ease of Use and Perceived Security and Privacy. Among these two, the domain Perceived Security and Privacy was found to have significant outcomes. Hence, this study reinforced that a WIoMT user intends to use the device only if he/she trusts the device; trust here has been defined in terms of its usefulness, easy to use and security and privacy features. This finding will be a steppingstone for equipment vendors and manufacturers to have a good grasp on the health industry, since the proper utilisation of WIoMT devices results in the effective and efficient management of health and wellbeing of users. The expected outcome from this research also aims to identify how users’ security and perception matters while adopting WIoMT, which in future can benefit security professionals to examine trust factors when implementing new and advanced WIoMT devices. Moreover, the expected result will help consumers as well as different healthcare industry to create a device which can be easily adopted and used securely by consumers

A Duration Analysis of the Time Taken to Find the First Job for Newly Arrived Migrants in Australia

This paper extends the traditional static focus of research on the labour market assimilation of migrants in Australia by analyzing the dynamics of job search and actual time taken to find the first job after arrival in Australia. The Longitudinal Survey of Immigrants to Australia (LSIA) covers two cohorts of recent migrants to Australia that differ considerably in immigration selection criteria and other policy settings, as well as in the macroeconomic employment conditions at their time of arrival in Australia. This gives rise to very different early labour market outcomes for the migrants in these two cohorts; and this paper looks at one specific aspect of this differing outcome – the time taken to find the first job after arrival in Australia. ¶ We analyze the inter-cohort differences in migrant characteristics and job search behaviour, and explicitly model the duration of the time taken to find the first job in Australia for the sub-sample of migrants who were the Principal Applicants in their visa applications. Using a conventional proportional hazards model framework, estimation results are presented for a Cox model specification and for a parameterized version of the baseline hazard which permits a formal test of equivalent hazards faced by the migrants in the two cohorts of LSIA. ¶ We find that the hazard rates of time to first job are determined by pre-immigrant characteristics, such as education and qualifications, recent work history in source country, the Australian visa categories, English language proficiency, and whether the migrants had previously visited Australia. The parametric model results show that both the underlying baseline hazards and the proportional hazard coefficients on most variables of interest differ significantly between Cohort 1 (arrived in Australia in 1993 through 1995) and Cohort 2 (arrived in Australia in 1999-2000). ¶ We then use the parametric model results to simulate the full distribution of the time taken to find the first job for these two migrant cohorts. We present alternative decompositions of the inter-cohort gap into effects due to differences in the observable characteristics of the migrants, and residual effects which can be attributed to different selection criteria and other policy settings and macro economic conditions that are applicable for the two time periods. ¶ The decomposition results suggest that the more favourable outcomes for Cohort 2 migrants are predominantly due to the setting of the Cohort 2 time period. This effect is most pronounced for the sample of female Principal Applicants. Cohort 1 migrants would also have experienced much quicker exits to a first job had they arrived under the macroeconomic and immigration policy setting of Cohort 2. Although the advantage derived from the Cohort 2 setting is not itself further decomposed, our analyses does indicated an important role for changes in migrating selection criteria to affect initial labour market outcomes of migrants after arrival in Australia