Health Investment over the Life-Cycle

We study the evolution of health investment over the life-cycle by calibrating a model of endogenous health accumulation. The model is able to produce the decline in labor supply with age as well as the hump-shaped consumption profile. In both cases, health and health investment play a crucial role as the former encroaches upon healthy time and the latter crowds out non-medical expenditures as people age. Finally, we quantify the value of health as both an investment and a consumption good. We show that the investment motive is about three times higher than the consumption motive during the early 20s, but decreases over the life-cycle until it disappears at retirement. In contrast, the consumption motive increases with age and surpasses the investment motive during the mid 40s.Health Investment, Consumption motive, investment motive, life-cycle

More Dynamic Data Structures for Geometric Set Cover with Sublinear Update Time

We study geometric set cover problems in dynamic settings, allowing insertions and deletions of points and objects. We present the first dynamic data structure that can maintain an O(1)-approximation in sublinear update time for set cover for axis-aligned squares in 2D . More precisely, we obtain randomized update time O(n^{2/3+?}) for an arbitrarily small constant ? > 0. Previously, a dynamic geometric set cover data structure with sublinear update time was known only for unit squares by Agarwal, Chang, Suri, Xiao, and Xue [SoCG 2020]. If only an approximate size of the solution is needed, then we can also obtain sublinear amortized update time for disks in 2D and halfspaces in 3D . As a byproduct, our techniques for dynamic set cover also yield an optimal randomized O(nlog n)-time algorithm for static set cover for 2D disks and 3D halfspaces, improving our earlier O(nlog n(log log n)^{O(1)}) result [SoCG 2020]

The Impact of Demographic Factors on Household Expenditures in Education and Health facilities

In consideration of significant roles played by consumption patterns in understanding the household living standards and indicating the person’s welfare and well-being, this study provides an up to date verification of the impact of demographic factors on consumers’ expenditure patterns in education and health in Tanzania. Using cross section data from the 2011-2012 household budget survey, the study empirically analyzed this impact. Three considered demographic factors were found to have a significant positive impact on households spending patterns on education and health services. The findings of this study will increase the economic actors’ understanding of the factors determining expenditure patterns and use them to evaluate the consumption and welfare of the population in Tanzania

Enclosing Points with Geometric Objects

Let $X$ be a set of points in $\mathbb{R}^2$ and $\mathcal{O}$ be a set of geometric objects in $\mathbb{R}^2$, where $|X| + |\mathcal{O}| = n$. We study the problem of computing a minimum subset $\mathcal{O}^* \subseteq \mathcal{O}$ that encloses all points in $X$. Here a point $x \in X$ is enclosed by $\mathcal{O}^*$ if it lies in a bounded connected component of $\mathbb{R}^2 \backslash (\bigcup_{O \in \mathcal{O}^*} O)$. We propose two algorithmic frameworks to design polynomial-time approximation algorithms for the problem. The first framework is based on sparsification and min-cut, which results in $O(1)$-approximation algorithms for unit disks, unit squares, etc. The second framework is based on LP rounding, which results in an $O(\alpha(n)\log n)$-approximation algorithm for segments, where $\alpha(n)$ is the inverse Ackermann function, and an $O(\log n)$-approximation algorithm for disks.Comment: In SoCG'2

Further Results on Colored Range Searching

We present a number of new results about range searching for colored (or "categorical") data: 1. For a set of $n$ colored points in three dimensions, we describe randomized data structures with $O(n\mathop{\rm polylog}n)$ space that can report the distinct colors in any query orthogonal range (axis-aligned box) in $O(k\mathop{\rm polyloglog} n)$ expected time, where $k$ is the number of distinct colors in the range, assuming that coordinates are in $\{1,\ldots,n\}$. Previous data structures require $O(\frac{\log n}{\log\log n} + k)$ query time. Our result also implies improvements in higher constant dimensions. 2. Our data structures can be adapted to halfspace ranges in three dimensions (or circular ranges in two dimensions), achieving $O(k\log n)$ expected query time. Previous data structures require $O(k\log^2n)$ query time. 3. For a set of $n$ colored points in two dimensions, we describe a data structure with $O(n\mathop{\rm polylog}n)$ space that can answer colored "type-2" range counting queries: report the number of occurrences of every distinct color in a query orthogonal range. The query time is $O(\frac{\log n}{\log\log n} + k\log\log n)$, where $k$ is the number of distinct colors in the range. Naively performing $k$ uncolored range counting queries would require $O(k\frac{\log n}{\log\log n})$ time. Our data structures are designed using a variety of techniques, including colored variants of randomized incremental construction (which may be of independent interest), colored variants of shallow cuttings, and bit-packing tricks.Comment: full version of a SoCG'20 pape

On the Fine-Grained Complexity of Small-Size Geometric Set Cover and Discrete k-Center for Small k

We study the time complexity of the discrete k-center problem and related (exact) geometric set cover problems when k or the size of the cover is small. We obtain a plethora of new results: - We give the first subquadratic algorithm for rectilinear discrete 3-center in 2D, running in O?(n^{3/2}) time. - We prove a lower bound of ?(n^{4/3-?}) for rectilinear discrete 3-center in 4D, for any constant ? > 0, under a standard hypothesis about triangle detection in sparse graphs. - Given n points and n weighted axis-aligned unit squares in 2D, we give the first subquadratic algorithm for finding a minimum-weight cover of the points by 3 unit squares, running in O?(n^{8/5}) time. We also prove a lower bound of ?(n^{3/2-?}) for the same problem in 2D, under the well-known APSP Hypothesis. For arbitrary axis-aligned rectangles in 2D, our upper bound is O?(n^{7/4}). - We prove a lower bound of ?(n^{2-?}) for Euclidean discrete 2-center in 13D, under the Hyperclique Hypothesis. This lower bound nearly matches the straightforward upper bound of O?(n^?), if the matrix multiplication exponent ? is equal to 2. - We similarly prove an ?(n^{k-?}) lower bound for Euclidean discrete k-center in O(k) dimensions for any constant k ? 3, under the Hyperclique Hypothesis. This lower bound again nearly matches known upper bounds if ? = 2. - We also prove an ?(n^{2-?}) lower bound for the problem of finding 2 boxes to cover the largest number of points, given n points and n boxes in 12D . This matches the straightforward near-quadratic upper bound

A molecular mechanism of chaperone–client recognition

Molecular chaperones are essential in aiding client proteins to fold into their native structure and in maintaining cellular protein homeostasis. However, mechanistic aspects of chaperone function are still not well understood at the atomic level. We use nuclear magnetic resonance spectroscopy to elucidate the mechanism underlying client recognition by the adenosine triphosphate-independent chaperone Spy at the atomic level and derive a structural model for the chaperone-client complex. Spy interacts with its partially folded client Im7 by selective recognition of flexible, locally frustrated regions in a dynamic fashion. The interaction with Spy destabilizes a partially folded client but spatially compacts an unfolded client conformational ensemble. By increasing client backbone dynamics, the chaperone facilitates the search for the native structure. A comparison of the interaction of Im7 with two other chaperones suggests that the underlying principle of recognizing frustrated segments is of a fundamental nature