On the multiple unicast capacity of 3-source, 3-terminal directed acyclic networks

We consider the multiple unicast problem with three source-terminal pairs over directed acyclic networks with unit-capacity edges. The three $s_i-t_i$ pairs wish to communicate at unit-rate via network coding. The connectivity between the $s_i - t_i$ pairs is quantified by means of a connectivity level vector, $[k_1 k_2 k_3]$ such that there exist $k_i$ edge-disjoint paths between $s_i$ and $t_i$. In this work we attempt to classify networks based on the connectivity level. It can be observed that unit-rate transmission can be supported by routing if $k_i \geq 3$, for all $i = 1, \dots, 3$. In this work, we consider, connectivity level vectors such that $\min_{i = 1, \dots, 3} k_i < 3$. We present either a constructive linear network coding scheme or an instance of a network that cannot support the desired unit-rate requirement, for all such connectivity level vectors except the vector $[1~2~4]$ (and its permutations). The benefits of our schemes extend to networks with higher and potentially different edge capacities. Specifically, our experimental results indicate that for networks where the different source-terminal paths have a significant overlap, our constructive unit-rate schemes can be packed along with routing to provide higher throughput as compared to a pure routing approach.Comment: To appear in the IEEE/ACM Transactions on Networkin

Minimum cost mirror sites using network coding: Replication vs. coding at the source nodes

Content distribution over networks is often achieved by using mirror sites that hold copies of files or portions thereof to avoid congestion and delay issues arising from excessive demands to a single location. Accordingly, there are distributed storage solutions that divide the file into pieces and place copies of the pieces (replication) or coded versions of the pieces (coding) at multiple source nodes. We consider a network which uses network coding for multicasting the file. There is a set of source nodes that contains either subsets or coded versions of the pieces of the file. The cost of a given storage solution is defined as the sum of the storage cost and the cost of the flows required to support the multicast. Our interest is in finding the storage capacities and flows at minimum combined cost. We formulate the corresponding optimization problems by using the theory of information measures. In particular, we show that when there are two source nodes, there is no loss in considering subset sources. For three source nodes, we derive a tight upper bound on the cost gap between the coded and uncoded cases. We also present algorithms for determining the content of the source nodes.Comment: IEEE Trans. on Information Theory (to appear), 201

An Achievable Region for the Double Unicast Problem Based on a Minimum Cut Analysis

We consider the multiple unicast problem under network coding over directed acyclic networks when there are two source-terminal pairs, s1 - t1 and s2 - t2. Current characterizations of the multiple unicast capacity region in this setting have a large number of inequalities, which makes them hard to explicitly evaluate. In this work we consider a slightly different problem. We assume that we only know certain minimum cut values for the network, e.g., mincut(Si, Tj), where Si ⊆ {si, s2} and Tj ⊆ {t1, t2} for different subsets Si and Tj. Based on these values, we propose an achievable rate region for this problem based on linear codes. Towards this end, we begin by defining a base region where both sources are multicast to both the terminals. Following this we enlarge the region by appropriately encoding the information at the source nodes, such that terminal ti is only guaranteed to decode information from the intended source si, while decoding a linear function of the other source. The rate region takes different forms depending upon the relationship of the different cut values in the network

SincNet-Based Hybrid Neural Network for Motor Imagery EEG Decoding.

It is difficult to identify optimal cut-off frequencies for filters used with the common spatial pattern (CSP) method in motor imagery (MI)-based brain-computer interfaces (BCIs). Most current studies choose filter cut-frequencies based on experience or intuition, resulting in sub-optimal use of MI-related spectral information in the electroencephalography (EEG). To improve information utilization, we propose a SincNet-based hybrid neural network (SHNN) for MI-based BCIs. First, raw EEG is segmented into different time windows and mapped into the CSP feature space. Then, SincNets are used as filter bank band-pass filters to automatically filter the data. Next, we used squeeze-and-excitation modules to learn a sparse representation of the filtered data. The resulting sparse data were fed into convolutional neural networks to learn deep feature representations. Finally, these deep features were fed into a gated recurrent unit module to seek sequential relations, and a fully connected layer was used for classification. We used the BCI competition IV datasets 2a and 2b to verify the effectiveness of our SHNN method. The mean classification accuracies (kappa values) of our SHNN method are 0.7426 (0.6648) on dataset 2a and 0.8349 (0.6697) on dataset 2b, respectively. The statistical test results demonstrate that our SHNN can significantly outperform other state-of-the-art methods on these datasets

Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems

Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating, and enabling our understanding of natural phenomena at a wide range of spatial and temporal scales, giving rise to a new area of research known as AI for science (AI4Science). Being an emerging research paradigm, AI4Science is unique in that it is an enormous and highly interdisciplinary area. Thus, a unified and technical treatment of this field is needed yet challenging. This work aims to provide a technically thorough account of a subarea of AI4Science; namely, AI for quantum, atomistic, and continuum systems. These areas aim at understanding the physical world from the subatomic (wavefunctions and electron density), atomic (molecules, proteins, materials, and interactions), to macro (fluids, climate, and subsurface) scales and form an important subarea of AI4Science. A unique advantage of focusing on these areas is that they largely share a common set of challenges, thereby allowing a unified and foundational treatment. A key common challenge is how to capture physics first principles, especially symmetries, in natural systems by deep learning methods. We provide an in-depth yet intuitive account of techniques to achieve equivariance to symmetry transformations. We also discuss other common technical challenges, including explainability, out-of-distribution generalization, knowledge transfer with foundation and large language models, and uncertainty quantification. To facilitate learning and education, we provide categorized lists of resources that we found to be useful. We strive to be thorough and unified and hope this initial effort may trigger more community interests and efforts to further advance AI4Science

Network coding for multiple unicast over directed acyclic networks

In a network that supports multiple unicast, there are several source terminal pairs; each source wishes to communicate with its corresponding terminal. Multiple unicast connections form bulk of the traffic over both wired and wireless networks. Thus, network coding schemes that can help improve network throughput for multiple unicasts are of considerable interest. In this dissertation, we consider the multiple unicast problem over directed acyclic networks with unit-capacity edges when there are three source terminal pairs and two source terminal pairs. For three unicast problem, we assume that the three s_i-t_i pairs wish to communicate at unit-rate via network coding. We define the connectivity level vector [k_1 k_2 k_3] such that there exist k_i edge-disjoint paths between s_i and t_i. We attempt to classify networks based on the connectivity level. We identify certain feasible and infeasible connectivity levels [k_1 k_2 k_3] for unit rate transmission. For the feasible cases, we construct schemes based on linear network coding. For the infeasible cases, we provide counter-examples, i.e., instances of graphs where the multiple unicast cannot be supported under any (potentially nonlinear) network coding scheme. For two unicast problem, we assume that we only know certain minimum cut values for the network, e.g., mincut(S_i, T_j), where S_i is a subset of (s_1, s_2) and T_j is a subset of (t_1, t_2) for different subsets S_i and T_j. Based on these values, we propose an achievable rate region for this problem using linear network codes. Towards this end, we begin by defining a multicast region where both sources are multicast to both the terminals. Following this we enlarge the region by appropriately encoding the information at the source nodes, such that terminal t_i is only guaranteed to decode information from the intended source s_i, while decoding a linear function of the other source.The rate region depends upon the relationship of the different cut values in the network.</p

Tracking technology innovation with multi-dimensional data aggregation

Current markets are becoming more diverse as a result of rapid technological and economic development. When customers want to buy something, they are frequently perplexed by dazzling products. People find it difficult to choose from thousands of products due to the market’s diversity. Choosing from a plethora of options is becoming increasingly time-consuming and complicated. It is possible to spend an hour deciding where to eat lunch. This issue is becoming more serious as the market's diversity grows. In the expanding market, there are more options. Furthermore, because each industry has a large number of companies that sell similar products, it is difficult to track the rate of development for a specific category of products. However, there are numerous benefits to tracking development trends. Companies can use the trend to predict the strengths and weaknesses of their competitors. They can also monitor the entire market to predict whether a technology is approaching a bottleneck or still has a lot of room to grow, allowing companies to better plan their future research. In the modern society, data can be found around every corner and it is easy to approach. If used correctly, people can discover many secrets and gain insights into massive databases. They can not only provide a better picture of the situation and tell how things are going, but they can also provide advice on how to make decisions and create plans to achieve specific goals in the business world. Nonetheless, in the majority of everyday situations, more than one criterion and attribute can be considered. For example, when a family wishes to travel and select the best location for themselves. There are numerous factors to consider, such as local food, attractions, price, holiday traffic, and so on. Even if they do not have a data analysis method, they will still have a similar system in their heads and weigh these various factors to see which are more critical for them and which are not. This paper seeks to introduce Analytic Hierarchy Process (referred as AHP) approach on data aggregation for multi-level and multi-criteria data. This project uses smartphone as a case study to present how the aggregation process works. The AHP method is based on this line of thought. Users can get the best decision using this method simply by answering a few questions that will be used to determine the weightages of all influencing factors. The system will do the rest. It will collect the scores for each factor and associate them with their respective weightages, resulting in an overall score for each travel destination in the previous travel place selection situation. The one with the highest score is the best option for this family at this time. This is a high-level overview of AHP methodology. This paper uses a smartphone as a case study to demonstrate this data aggregation method in depth.Bachelor of Engineering (Mechanical Engineering