Stability Region of a Slotted Aloha Network with K-Exponential Backoff

Stability region of random access wireless networks is known for only simple network scenarios. The main problem in this respect is due to interaction among queues. When transmission probabilities during successive transmissions change, e.g., when exponential backoff mechanism is exploited, the interactions in the network are stimulated. In this paper, we derive the stability region of a buffered slotted Aloha network with K-exponential backoff mechanism, approximately, when a finite number of nodes exist. To this end, we propose a new approach in modeling the interaction among wireless nodes. In this approach, we model the network with inter-related quasi-birth-death (QBD) processes such that at each QBD corresponding to each node, a finite number of phases consider the status of the other nodes. Then, by exploiting the available theorems on stability of QBDs, we find the stability region. We show that exponential backoff mechanism is able to increase the area of the stability region of a simple slotted Aloha network with two nodes, more than 40\%. We also show that a slotted Aloha network with exponential backoff may perform very near to ideal scheduling. The accuracy of our modeling approach is verified by simulation in different conditions.Comment: 30 pages, 6 figure

Representation Learning for Clustering: A Statistical Framework

We address the problem of communicating domain knowledge from a user to the designer of a clustering algorithm. We propose a protocol in which the user provides a clustering of a relatively small random sample of a data set. The algorithm designer then uses that sample to come up with a data representation under which $k$-means clustering results in a clustering (of the full data set) that is aligned with the user's clustering. We provide a formal statistical model for analyzing the sample complexity of learning a clustering representation with this paradigm. We then introduce a notion of capacity of a class of possible representations, in the spirit of the VC-dimension, showing that classes of representations that have finite such dimension can be successfully learned with sample size error bounds, and end our discussion with an analysis of that dimension for classes of representations induced by linear embeddings.Comment: To be published in Proceedings of UAI 201

Sample-Efficient Learning of Mixtures

We consider PAC learning of probability distributions (a.k.a. density estimation), where we are given an i.i.d. sample generated from an unknown target distribution, and want to output a distribution that is close to the target in total variation distance. Let $\mathcal F$ be an arbitrary class of probability distributions, and let $\mathcal{F}^k$ denote the class of $k$-mixtures of elements of $\mathcal F$. Assuming the existence of a method for learning $\mathcal F$ with sample complexity $m_{\mathcal{F}}(\epsilon)$, we provide a method for learning $\mathcal F^k$ with sample complexity $O({k\log k \cdot m_{\mathcal F}(\epsilon) }/{\epsilon^{2}})$. Our mixture learning algorithm has the property that, if the $\mathcal F$-learner is proper/agnostic, then the $\mathcal F^k$-learner would be proper/agnostic as well. This general result enables us to improve the best known sample complexity upper bounds for a variety of important mixture classes. First, we show that the class of mixtures of $k$ axis-aligned Gaussians in $\mathbb{R}^d$ is PAC-learnable in the agnostic setting with $\widetilde{O}({kd}/{\epsilon ^ 4})$ samples, which is tight in $k$ and $d$ up to logarithmic factors. Second, we show that the class of mixtures of $k$ Gaussians in $\mathbb{R}^d$ is PAC-learnable in the agnostic setting with sample complexity $\widetilde{O}({kd^2}/{\epsilon ^ 4})$, which improves the previous known bounds of $\widetilde{O}({k^3d^2}/{\epsilon ^ 4})$ and $\widetilde{O}(k^4d^4/\epsilon ^ 2)$ in its dependence on $k$ and $d$. Finally, we show that the class of mixtures of $k$ log-concave distributions over $\mathbb{R}^d$ is PAC-learnable using $\widetilde{O}(d^{(d+5)/2}\epsilon^{-(d+9)/2}k)$ samples.Comment: A bug from the previous version, which appeared in AAAI 2018 proceedings, is fixed. 18 page

A programmable photonic memory

The significant advancements in integrated photonics have enabled high-speed and energy efficient systems for various applications from data communications and high-performance computing, to medical diagnosis, sensing and ranging. However, data storage in these systems has been dominated by electronic memories which necessitates signal conversion between optical and electrical as well as analog and digital domains, and data movement between processor and memory that reduce the speed and energy efficiency. To date, a scalable optical memory with optical control has remained an open problem. Here we report an integrated photonic set-reset latch as a fundamental optical static memory unit based on universal optical logic gates. While the proposed memory is compatible with different photonic platforms, its functionality is demonstrated on a programmable silicon photonic chip as a proof of concept. Optical set, reset, and complementary outputs, scalability to a large number of memory units via the independent latch supply light, and compatibility with different photonic platforms enable more efficient and lower latency optical processing systems

A novel class of scheduling policies for the stochastic resource-constrained project scheduling problem.

We study the resource-constrained project scheduling problem with stochastic activity durations. We introduce a new class of scheduling policies for this problem, which make a number of a-priori sequencing decisions in a pre-processing phase, while the remaining decisions are made dynamically during project execution. The pre-processing decisions entail the addition of precedence constraints to the scheduling instance, hereby resolving some potential resource conflicts. We compare the performance of this new class with existing scheduling policies for the stochastic resource-constrained project scheduling problem, and we observe that the new class is significantly better when the variability in the activity durations is medium to high.Project scheduling; Uncertainty; Stochastic activity durations; Scheduling policies;

RNA catalysis in model protocell vesicles.

We are engaged in a long-term effort to synthesize chemical systems capable of Darwinian evolution, based on the encapsulation of self-replicating nucleic acids in self-replicating membrane vesicles. Here, we address the issue of the compatibility of these two replicating systems. Fatty acids form vesicles that are able to grow and divide, but vesicles composed solely of fatty acids are incompatible with the folding and activity of most ribozymes, because low concentrations of divalent cations (e.g., Mg(2+)) cause fatty acids to precipitate. Furthermore, vesicles that grow and divide must be permeable to the cations and substrates required for internal metabolism. We used a mixture of myristoleic acid and its glycerol monoester to construct vesicles that were Mg(2+)-tolerant and found that Mg(2+) cations can permeate the membrane and equilibrate within a few minutes. In vesicles encapsulating a hammerhead ribozyme, the addition of external Mg(2+) led to the activation and self-cleavage of the ribozyme molecules. Vesicles composed of these amphiphiles grew spontaneously through osmotically driven competition between vesicles, and further modification of the membrane composition allowed growth following mixed micelle addition. Our results show that membranes made from simple amphiphiles can form vesicles that are stable enough to retain encapsulated RNAs in the presence of divalent cations, yet dynamic enough to grow spontaneously and allow the passage of Mg(2+) and mononucleotides without specific macromolecular transporters. This combination of stability and dynamics is critical for building model protocells in the laboratory and may have been important for early cellular evolution

Ethnicity, Culture, And Mental Health Among College Students Of Middle Eastern Heritage

Depression is a significant mental health issue in American college students. However, as is the case for other minority students, this topic has been little studied in students of Middle Eastern background. Stigma and negative attitudes toward seeking mental health services are a big part of Middle Eastern culture, which reduces the chances that this population will seek treatment when they need it. In addition, it is important to study the relationship between ethnic identity and psychological functioning, because ethnic identity could serve as a protective factor against depression in persons of Middle Eastern descent. A strong cultural identity is thought to have that effect for persons of other minority groups in this country. The current study explored depression symptoms in Middle Eastern, African American, and Caucasian college students. No group differences were found in level of depression symptoms. As expected, Middle Eastern college students had more negative attitudes toward seeking mental health services than African American and Caucasian students. Among the African Americans and Caucasians, stronger ethnic identity was associated with lower presence of depression symptoms when controlling for gender, age, and social desirability; however, this relationship was not significant among the Middle Eastern and African American students. Research on minority college students could provide greater insight into their current needs, allowing policy makers to implement appropriate interventions for minority individuals. These findings indicate that Middle Eastern students may have characteristics related to their mental health that are not well represented by most research in the more commonly studied ethnic groups among American college students

Parental Ptsd, Emotion Regulation, And Behavior Problems In Toddlerhood: Unique Associations Among Families In Urban Poverty

Parental posttraumatic stress disorder (PTSD) has been shown to negatively impact children’s socioemotional development (Schwerdtfeger et al., 2014) and increase children’s risk for later psychopathology (Scheeringa & Zeanah, 2008; Yehuda, Halligan, & Bierer, 2001). Less is known about this topic among minority and poor mothers and fathers of toddlers, and the critical role parents’ emotion regulation may play in mediating the associations between PTSD and toddlers’ socioemotional problems (Beck et al., 2009). Parental emotion dysregulation has been linked with children’s socioemotional problems (Coyne & Thompson, 2011), especially during toddlerhood when children are beginning to learn how to regulate their own emotions (Kopp, 1989). Evaluating both mothers’ and fathers’ PTSD, emotion regulation, and child behavior problems during toddlerhood is particularly important among urban populations due to high risk of trauma exposure (Evans & English, 2002). The current study aimed to examine internalizing and externalizing behavior problems in toddlers from low-income families, evaluating whether and how mothers’ and fathers’ PTSD, emotion regulation, and parenting are associated with toddler behavioral problems. It was hypothesized that the relationship between parents’ PTSD and toddlers’ internalizing and externalizing problems will be mediated by parents’ emotion regulation and parenting quality. The current study describes data from a broader study of socioemotional development of toddlerhood among urban families (N=96). Mothers and fathers reported on their own PTSD symptoms (PDS; Foa et al., 1997), depression (CES-D; Radloff, 1977), emotion regulation (EDS, Conklin et al., 2006), and their toddlers’ behavior problems (CBCL; Achenbach & Rescorla, 2001). Parenting quality was coded based on observational data from a family drawing task, during which families drew pictures of happy and sad times they have had as a family. Children’s internalizing and externalizing problems were calculated by averaging the CBCL scores reported by both parents. Primary analyses were conducted using Hayes PROCESS macro for multiple mediation (model 6; Hayes, 2013), controlling for maternal and paternal depression, and cumulative demographic risk. Findings indicated that (1) both mothers’ and fathers’ emotion regulation and depression, but not PTSD and parenting, were the main parental factors linked to higher internalizing behavior problems in toddlers, and only mothers’ cumulative demographic risk was significantly associated with toddlers’ externalizing behavior problems; (2) the associations between parental PTSD and child behavior problems was not mediated through emotion regulation and parenting; (3) fathers’ symptoms of emotion dysregulation and depression were as equally important in predicting toddler behavior problems as mothers’ emotion dysregulation and depression; (4) parental PTSD, emotion dysregulation, and depression were more strongly associated with toddlers’ internalizing problems than their externalizing problems. Findings provide support for the negative impact of maternal and paternal emotion dysregulation, depression, and cumulative demographic risk on toddler internalizing and externalizing problems among low-income families and offer insight into essential avenues to implement interventions. Although parents’ PTSD symptoms may have an impact on toddlers’ behavior problems, their emotional dysregulation plays a more significant role. The focus mediator, paternal emotion regulation, appears to be a concrete target for clinical assessment and treatment