Abstract:
Significant physiological switches occur at birth such as the transition from fetal parallel blood flow to a two-circuit serial system with increased arterial oxygenation of blood delivered to all organs including the brain. In addition, the extra-uterine environment exposes premature infants to a host of stimuli. These events could conceivably alter the trajectory of brain development in premature infants. We used in vivo magnetic resonance spectroscopy to measure absolute brain metabolite concentrations in term and premature-born infants without evidence of brain injury at equivalent post-conceptional age. Prematurity altered the developmental time courses of N-acetyl-aspartate, a marker for axonal and neuronal development, creatine, an energy metabolite, and choline, a membrane metabolite, in parietal white matter. Specifically, at term-equivalency, metabolic maturation in preterm infants preceded development in term infants, but then progressed at a slower pace and trajectories merged at ≈340–370 post-conceptional days. In parieto/occipital grey matter similar trends were noticed but statistical significance was not reached. The timing of white matter development and synchronization of white matter and grey matter maturation in premature-born infants is disturbed. This may contribute to the greater risk of long-term neurological problems of premature infants and to their higher risk for white matter injury.

Abstract:
We study the problem of covering a given set of $n$ points in a high, $d$-dimensional space by the minimum enclosing polytope of a given arbitrary shape. We present algorithms that work for a large family of shapes, provided either only translations and no rotations are allowed, or only rotation about a fixed point is allowed; that is, one is allowed to only scale and translate a given shape, or scale and rotate the shape around a fixed point. Our algorithms start with a polytope guessed to be of optimal size and iteratively moves it based on a greedy principle: simply move the current polytope directly towards any outside point till it touches the surface. For computing the minimum enclosing ball, this gives a simple greedy algorithm with running time $O(nd/\eps)$ producing a ball of radius $1+\eps$ times the optimal. This simple principle generalizes to arbitrary convex shape when only translations are allowed, requiring at most $O(1/\eps^2)$ iterations. Our algorithm implies that {\em core-sets} of size $O(1/\eps^2)$ exist not only for minimum enclosing ball but also for any convex shape with a fixed orientation. A {\em Core-Set} is a small subset of $poly(1/\eps)$ points whose minimum enclosing polytope is almost as large as that of the original points. Although we are unable to combine our techniques for translations and rotations for general shapes, for the min-cylinder problem, we give an algorithm similar to the one in \cite{HV03}, but with an improved running time of $2^{O(\frac{1}{\eps^2}\log \frac{1}{\eps})} nd$.

Abstract:
In this paper we study the problem of finding the approximate nearest neighbor of a query point in the high dimensional space, focusing on the Euclidean space. The earlier approaches use locality-preserving hash functions (that tend to map nearby points to the same value) to construct several hash tables to ensure that the query point hashes to the same bucket as its nearest neighbor in at least one table. Our approach is different -- we use one (or a few) hash table and hash several randomly chosen points in the neighborhood of the query point showing that at least one of them will hash to the bucket containing its nearest neighbor. We show that the number of randomly chosen points in the neighborhood of the query point $q$ required depends on the entropy of the hash value $h(p)$ of a random point $p$ at the same distance from $q$ at its nearest neighbor, given $q$ and the locality preserving hash function $h$ chosen randomly from the hash family. Precisely, we show that if the entropy $I(h(p)|q,h) = M$ and $g$ is a bound on the probability that two far-off points will hash to the same bucket, then we can find the approximate nearest neighbor in $O(n^\rho)$ time and near linear $\tilde O(n)$ space where $\rho = M/\log(1/g)$. Alternatively we can build a data structure of size $\tilde O(n^{1/(1-\rho)})$ to answer queries in $\tilde O(d)$ time. By applying this analysis to the locality preserving hash functions in and adjusting the parameters we show that the $c$ nearest neighbor can be computed in time $\tilde O(n^\rho)$ and near linear space where $\rho \approx 2.06/c$ as $c$ becomes large.

Abstract:
The study of hashing is closely related to the analysis of balls and bins. It is well-known that instead of using a single hash function if we randomly hash a ball into two bins and place it in the smaller of the two, then this dramatically lowers the maximum load on bins. This leads to the concept of two-way hashing where the largest bucket contains $O(\log\log n)$ balls with high probability. The hash look up will now search in both the buckets an item hashes to. Since an item may be placed in one of two buckets, we could potentially move an item after it has been initially placed to reduce maximum load. with a maximum load of We show that by performing moves during inserts, a maximum load of 2 can be maintained on-line, with high probability, while supporting hash update operations. In fact, with $n$ buckets, even if the space for two items are pre-allocated per bucket, as may be desirable in hardware implementations, more than $n$ items can be stored giving a high memory utilization. We also analyze the trade-off between the number of moves performed during inserts and the maximum load on a bucket. By performing at most $h$ moves, we can maintain a maximum load of $O(\frac{\log \log n}{h \log(\log\log n/h)})$. So, even by performing one move, we achieve a better bound than by performing no moves at all.

Abstract:
Can (scientific) knowledge be reliably preserved over the long term? We have today very efficient and reliable methods to encode, store and retrieve data in a storage medium that is fault tolerant against many types of failures. But does this guarantee -- or does it even seem likely -- that all knowledge can be preserved over thousands of years and beyond? History shows that many types of knowledge that were known before have been lost. We observe that the nature of stored and communicated information and the way it is interpreted is such that it always tends to decay and therefore must lost eventually in the long term. The likely fundamental conclusion is that knowledge cannot be reliably preserved indefinitely.

Abstract:
The paper explores known results related to the problem of identifying if a given program terminates on all inputs -- this is a simple generalization of the halting problem. We will see how this problem is related and the notion of proof verifiers. We also see how verifying if a program is terminating involves reasoning through a tower of axiomatic theories -- such a tower of theories is known as Turing progressions and was first studied by Alan Turing in the 1930's. We will see that this process has a natural connection to ordinal numbers. The paper is presented from the perspective of a non-expert in the field of logic and proof theory.

Abstract:
We report a female with PRS (micrognathia, cleft palate), microcephaly, ocular hypertelorism, mental retardation and bilateral hearing loss, who at age 15 was also diagnosed with severe NF2 (bilateral cerebellopontine schwannomas and multiple extramedullary/intradural spine tumors). This is the first published report of an individual with both diagnosed PRS and NF2. High resolution karyotype revealed 46, XX, del(22)(q12.1q12.3), FISH confirmed a deletion encompassing NF2, and chromosomal microarray identified a 3,693 kb deletion encompassing multiple genes including NF2 and MN1 (meningioma 1).Five additional patients with craniofacial dysmorphism and deletion in chromosome 22-adjacent-to or containing NF2 were identified in PubMed and the DECIPHER clinical chromosomal database. Their shared chromosomal deletion encompassed MN1, PITPNB and TTC28. MN1, initially cloned from a patient with meningioma, is an oncogene in murine hematopoiesis and participates as a fusion gene (TEL/MN1) in human myeloid leukemias. Interestingly, Mn1-haploinsufficient mice have abnormal skull development and secondary cleft palate. Additionally, Mn1 regulates maturation and function of calvarial osteoblasts and is an upstream regulator of Tbx22, a gene associated with murine and human cleft palate. This suggests that deletion of MN1 in the six patients we describe may be causally linked to their cleft palates and/or craniofacial abnormalities.Thus, our report describes a NF2-adjacent chromosome 22q12.2 deletion syndrome and is the first to report association of MN1 deletion with abnormal craniofacial development and/or cleft palate in humans.Pierre-Robin sequence (PRS) refers to a combination of micrognathia or retrognathia, glossoptosis and respiratory distress, with or without cleft palate, named after the French stomatologist, Pierre Robin [1-5]. The incidence of PRS is estimated at 1 in 8,500-14,000 births and continues to be associated with high morbidity secondary to a compromised air

Abstract:
Many children born preterm exhibit frontal executive dysfunction, behavioral problems including attentional deficit/hyperactivity disorder and attention related learning disabilities. Anomalies in regional specificity of cortico-striato-thalamo-cortical circuits may underlie deficits in these disorders. Nonspecific volumetric deficits of striatal structures have been documented in these subjects, but little is known about surface deformation in these structures. For the first time, here we found regional surface morphological differences in the preterm neonatal ventral striatum. We performed regional group comparisons of the surface anatomy of the striatum (putamen and globus pallidus) between 17 preterm and 19 term-born neonates at term-equivalent age. We reconstructed striatal surfaces from manually segmented brain magnetic resonance images and analyzed them using our in-house conformal mapping program. All surfaces were registered to a template with a new surface fluid registration method. Vertex-based statistical comparisons between the two groups were performed via four methods: univariate and multivariate tensor-based morphometry, the commonly used medial axis distance, and a combination of the last two statistics. We found statistically significant differences in regional morphology between the two groups that are consistent across statistics, but more extensive for multivariate measures. Differences were localized to the ventral aspect of the striatum. In particular, we found abnormalities in the preterm anterior/inferior putamen, which is interconnected with the medial orbital/prefrontal cortex and the midline thalamic nuclei including the medial dorsal nucleus and pulvinar. These findings support the hypothesis that the ventral striatum is vulnerable, within the cortico-stiato-thalamo-cortical neural circuitry, which may underlie the risk for long-term development of frontal executive dysfunction, attention deficit hyperactivity disorder and attention-related learning disabilities in preterm neonates.

Abstract:
Preterm infants (~10% of all births) are at high-risk for long-term neurodevelopmental disabilities, most often resulting from white matter injury sustained during the neonatal period. Glutamate excitotoxicity is hypothesized to be a key mechanism in the pathogenesis of white matter injury; however, there has been no in vivo demonstration of glutamate excitotoxicity in preterm infants. Using magnetic resonance spectroscopy (MRS), we tested the hypothesis that glutamate and glutamine, i.e., markers of glutamatergic metabolism, are altered in association with punctate white matter lesions and “diffuse excessive high signal intensity” (DEHSI), the predominant patterns of preterm white matter injury. We reviewed all clinically-indicated MRS studies conducted on preterm infants at a single institution during a six-year period and determined the absolute concentration of glutamate, glutamine, and four other key metabolites in the parietal white matter in 108 of those infants after two investigators independently evaluated the studies for punctate white matter lesions and DEHSI. Punctate white matter lesions were associated with a 29% increase in glutamine concentration (p = 0.002). In contrast, there were no differences in glutamatergic metabolism in association with DEHSI. Severe DEHSI, however, was associated with increased lactate concentration (p = 0.001), a marker of tissue acidosis. Findings from this study support glutamate excitotoxicity in the pathogenesis of punctate white matter lesions, but not necessarily in DEHSI, and suggest that MRS provides a useful biomarker for determining the pathogenesis of white matter injury in preterm infants during a period when neuroprotective agents may be especially effective.

Abstract:
In this paper, we study the two choice balls and bins process when balls are not allowed to choose any two random bins, but only bins that are connected by an edge in an underlying graph. We show that for $n$ balls and $n$ bins, if the graph is almost regular with degree $n^\epsilon$, where $\epsilon$ is not too small, the previous bounds on the maximum load continue to hold. Precisely, the maximum load is $\log \log n + O(1/\epsilon) + O(1)$. For general $\Delta$-regular graphs, we show that the maximum load is $\log\log n + O(\frac{\log n}{\log (\Delta/\log^4 n)}) + O(1)$ and also provide an almost matching lower bound of $\log \log n + \frac{\log n}{\log (\Delta \log n)}$. V{\"o}cking [Voc99] showed that the maximum bin size with $d$ choice load balancing can be further improved to $O(\log\log n /d)$ by breaking ties to the left. This requires $d$ random bin choices. We show that such bounds can be achieved by making only two random accesses and querying $d/2$ contiguous bins in each access. By grouping a sequence of $n$ bins into $2n/d$ groups, each of $d/2$ consecutive bins, if each ball chooses two groups at random and inserts the new ball into the least-loaded bin in the lesser loaded group, then the maximum load is $O(\log\log n/d)$ with high probability.