14 research outputs found
Parameterized Complexity of Fair Bisection: (FPT-Approximation meets Unbreakability)
No full textIn the Minimum Bisection problem input is a graph G and the goal is to partition the vertex set into two parts A and B, such that ||A|-|B|| ≤ 1 and the number k of edges between A and B is minimized. The problem is known to be NP-hard, and assuming the Unique Games Conjecture even NP-hard to approximate within a constant factor [Khot and Vishnoi, J.ACM'15]. On the other hand, a (log n)-approximation algorithm [Räcke, STOC'08] and a parameterized algorithm [Cygan et al., ACM Transactions on Algorithms'20] running in time k^(k) n^(1) is known.
The Minimum Bisection problem can be viewed as a clustering problem where edges represent similarity and the task is to partition the vertices into two equally sized clusters while minimizing the number of pairs of similar objects that end up in different clusters. Motivated by a number of egregious examples of unfair bias in AI systems, many fundamental clustering problems have been revisited and re-formulated to incorporate fairness constraints. In this paper we initiate the study of the Minimum Bisection problem with fairness constraints. Here the input is a graph G, positive integers c and k, a function χ:V(G) → {1, …, c} that assigns a color χ(v) to each vertex v in G, and c integers r_1,r_2,⋯,r_c. The goal is to partition the vertex set of G into two almost-equal sized parts A and B with at most k edges between them, such that for each color i ∈ {1, …, c}, A has exactly r_i vertices of color i. Each color class corresponds to a group which we require the partition (A, B) to treat fairly, and the constraints that A has exactly r_i vertices of color i can be used to encode that no group is over- or under-represented in either of the two clusters.
We first show that introducing fairness constraints appears to make the Minimum Bisection problem qualitatively harder. Specifically we show that unless FPT=W[1] the problem admits no f(c)n^(1) time algorithm even when k = 0. On the other hand, our main technical contribution shows that is that this hardness result is simply a consequence of the very strict requirement that each color class i has exactly r_i vertices in A. In particular we give an f(k,c,ε)n^(1) time algorithm that finds a balanced partition (A, B) with at most k edges between them, such that for each color i ∈ [c], there are at most (1±ε)r_i vertices of color i in A.
Our approximation algorithm is best viewed as a proof of concept that the technique introduced by [Lampis, ICALP'18] for obtaining FPT-approximation algorithms for problems of bounded tree-width or clique-width can be efficiently exploited even on graphs of unbounded width. The key insight is that the technique of Lampis is applicable on tree decompositions with unbreakable bags (as introduced in [Cygan et al., SIAM Journal on Computing'14]). An important ingredient of our approximation scheme is a combinatorial result that may be of independent interest, namely that for every k, every graph G admits a tree decomposition with adhesions of size at most (k), unbreakable bags, and logarithmic depth
Exact Exponential Algorithms for Clustering Problems
No full textIn this paper we initiate a systematic study of exact algorithms for some of the well known clustering problems, namely k-MEDIAN and k-MEANS. In k-MEDIAN, the input consists of a set X of n points belonging to a metric space, and the task is to select a subset C ⊆ X of k points as centers, such that the sum of the distances of every point to its nearest center is minimized. In k-MEANS, the objective is to minimize the sum of squares of the distances instead. It is easy to design an algorithm running in time max_{k ≤ n} {n choose k} n^(1) = ^*(2ⁿ) (here, ^*(⋅) notation hides polynomial factors in n). In this paper we design first non-trivial exact algorithms for these problems. In particular, we obtain an ^*((1.89)ⁿ) time exact algorithm for k-MEDIAN that works for any value of k. Our algorithm is quite general in that it does not use any properties of the underlying (metric) space - it does not even require the distances to satisfy the triangle inequality. In particular, the same algorithm also works for k-Means. We complement this result by showing that the running time of our algorithm is asymptotically optimal, up to the base of the exponent. That is, unless the Exponential Time Hypothesis fails, there is no algorithm for these problems running in time 2^o(n)⋅n^(1).
Finally, we consider the "facility location" or "supplier" versions of these clustering problems, where, in addition to the set X we are additionally given a set of m candidate centers (or facilities) F, and objective is to find a subset of k centers from F. The goal is still to minimize the k-Median/k-Means/k-Center objective. For these versions we give a (2ⁿ (mn)^(1)) time algorithms using subset convolution. We complement this result by showing that, under the Set Cover Conjecture, the "supplier" versions of these problems do not admit an exact algorithm running in time 2^{(1-ε) n} (mn)^(1)
Unsteady Fluid-structure Interactions in Soft-walled Microchannels
No full textA one-dimensional model is developed for the transient (unsteady) fluid--structure interaction (FSI) between a soft-walled microchannel and viscous fluid flow within it. An Euler–Bernoulli beam bending equation, which accounts for both transverse bending rigidity and nonlinear axial tension, is coupled to a one-dimensional fluid model obtained by depth-averaging (across the channel height) the two-dimensional incompressible Navier–Stokes equations. A novel feature of the proposed model is that the Navier–Stokes equations are scaled in the viscous (lubrication) limit relevant to microfluidics. The resulting set of coupled nonlinear partial differential equations are solved numerically through a segregated approach employing fully-implicit time stepping and second-order finite-differences for discretization of the various differential operators. Internal FSI iterations and under-relaxation are employed to handle the stiff nonlinear algebraic problems within each time step. Next, the Strouhal number (ratio of the solid to fluid characteristic time scales) is fixed at unity, while the Reynolds number Re (ratio of inertial to viscous fluid forces) and a non-dimensional Young\u27s modulus Σ are varied independently to explore the unsteady FSI behaviors in this parameter space. Based on the magnitude of the channel wall\u27s deformation, a critical Reynolds number is calculated for (a) pure bending and (b) both bending and tension, by determining when the maximum steady state deformation exceeds a certain threshold. This critical Reynolds number is shown to scale with Σ, specifically following the scaling of Re ∝ Σ3/4. This scaling indicates that “wall modes” play a role in the evolution of the system away from a flat-wall state, eventually leading to unsteady (transient) FSIs. Due to nonlinearity in the wall tension, an intermediate metastable state is found at “moderate” Reynolds numbers, which resembles a “buckling mode” of a beam, before the wall “snaps” into a final steady state. The maximum wall displacement at steady state is shown to correlate well with a single dimensionless group, namely Re/Σ0.9. The details of the collapse onto a single trend line depend on whether we consider (a) pure bending or (b) both bending and tension, nevertheless a clean collapse occurs for both. A discussion is given, on the basis of the numerical approach to the proposed one-dimensional unsteady FSI model, regarding the numerical difficulties in simulating stiff problems in a segregated approach. Finally, elaborating upon the last point, a critical discussion of current computational approaches in OpenFOAM for three-dimensional unsteady microfluidic FSIs is provided
A Ramsey theorem for the reals
No full textWe prove that for every colouring of pairs of reals with finitely-many
colours, there is a set homeomorphic to the rationals which takes no more than
two colours. This was conjectured by Galvin in 1970, and a colouring of
Sierpi{\'n}ski from 1933 witnesses that the number of colours cannot be reduced
to one. Previously in 1985 Shelah had shown that a stronger statement is
consistent with a forcing construction assuming the existence of large
cardinals. Then in 2018 Raghavan and Todor\v{c}evi\'c had proved it assuming
the existence of large cardinals. We prove it in . In fact Raghavan and
Todor\v{c}evi\'c proved, assuming more large cardinals, a similar result for a
large class of topological spaces. We prove this also, again in .Comment: Preliminary versio
FPT Approximations for Capacitated/Fair Clustering with Outliers
No full textClustering problems such as -Median, and -Means, are motivated from
applications such as location planning, unsupervised learning among others. In
such applications, it is important to find the clustering of points that is not
``skewed'' in terms of the number of points, i.e., no cluster should contain
too many points. This is modeled by capacity constraints on the sizes of
clusters. In an orthogonal direction, another important consideration in
clustering is how to handle the presence of outliers in the data. Indeed, these
clustering problems have been generalized in the literature to separately
handle capacity constraints and outliers. To the best of our knowledge, there
has been very little work on studying the approximability of clustering
problems that can simultaneously handle both capacities and outliers.
We initiate the study of the Capacitated -Median with Outliers (CMO)
problem. Here, we want to cluster all except outlier points into at most
clusters, such that (i) the clusters respect the capacity constraints, and
(ii) the cost of clustering, defined as the sum of distances of each
non-outlier point to its assigned cluster-center, is minimized.
We design the first constant-factor approximation algorithms for CMO. In
particular, our algorithm returns a (3+\epsilon)-approximation for CMO in
general metric spaces, and a (1+\epsilon)-approximation in Euclidean spaces of
constant dimension, that runs in time in time , where denotes the input size. We can also extend these
results to a broader class of problems, including Capacitated
k-Means/k-Facility Location with Outliers, and Size-Balanced Fair Clustering
problems with Outliers. For each of these problems, we obtain an approximation
ratio that matches the best known guarantee of the corresponding outlier-free
problem.Comment: Abstract shortened to meet arxiv requirement
Parameterized Complexity of Fair Bisection: FPT-Approximation meets Unbreakability
No full textIn the Minimum Bisection problem, input is a graph and the goal is to
partition the vertex set into two parts and , such that and the number of edges between and is minimized. This problem
can be viewed as a clustering problem where edges represent similarity, and the
task is to partition the vertices into two equally sized clusters, while
minimizing the number of pairs of similar objects that end up in different
clusters. In this paper, we initiate the study of a fair version of Minimum
Bisection. In this problem, the vertices of the graph are colored using one of
colors. The goal is to find a bisection with at most
edges between the parts, such that for each color , has exactly
vertices of color .
We first show that Fair Bisection is [1]-hard parameterized by even
when . On the other hand, our main technical contribution shows that is
that this hardness result is simply a consequence of the very strict
requirement that each color class has {\em exactly} vertices in .
In particular, we give an time algorithm that finds a
balanced partition with at most edges between them, such that for
each color , there are at most vertices of color
in . Our approximation algorithm is best viewed as a proof of concept
that the technique introduced by [Lampis, ICALP '18] for obtaining
FPT-approximation algorithms for problems of bounded tree-width or clique-width
can be efficiently exploited even on graphs of unbounded width. The key insight
is that the technique of Lampis is applicable on tree decompositions with
unbreakable bags (as introduced in [Cygan et al., SIAM Journal on Computing
'14]). Along the way, we also derive a combinatorial result regarding tree
decompositions of graphs.Comment: Full version of ESA 2023 paper. Abstract shortened to meet the
character limi
Development of Thin Heterojunction Solar Cells with High Open Circuit Voltage
No full textabstract: The aim of this thesis research is the development of thin silicon heterojunction solar cells with high open circuit voltage (Voc). Heterojunction solar cells are higher in efficiency than diffused junction c-Si solar cells, and they are less vulnerable to light degradation. Furthermore, the low temperature processing of heterojunction cells favour a decrease in production costs and improve cell performance at the same time. Since about 30 % of the module cost is a result of substrate cost, thin solar cells are of economic advantage than their thicker counterparts. This lead to the research for development of thin heterojunction solar cells. For high cell efficiencies and performance, it is important for cells to have a high operating voltage and Voc. Development of heterojunction cells with high Voc required a stable and repeatable baseline process on which further improvements could be made. Therefore a baseline process for heterojunction solar cells was developed and demonstrated as a pilot line at the Solar Power Lab at ASU. All the processes involved in fabrication of cells with the baseline process were optimized to have a stable and repeatable process. The cells produced with the baseline process were 19-20% efficient. The baseline process was further used as a backbone to improve and develop thin cells with even higher Voc. The process recipe was optimized with an aim to explore the limits of Voc that could be achieved with this structure on a much thinner substrate than used for the baseline process. A record Voc greater than 760mV was recorded at SPL using Suns-Voc tester on a 50 microns thick heterojunction cell without metallization. Furthermore, Voc of 754.2 mV was measured on a 50 microns thick cell with metallization by National Renewable Energy Laboratory (NREL), which is a record for Voc for heterojunction cells with metallization. High Voc corresponds to high cell efficiency and therefore, higher module voltage and power with using the same number of cells as compared to other c-Si solar cells.Dissertation/ThesisMasters Thesis Electrical Engineering 201
Macrobrachium ramae Das & Pahari & Bhattacharya 2021, sp. nov.
No full textMacrobrachium ramae sp. nov. (Fig. 1–3) Materials examined. Measurements (in mm), HOLOTYPE (1♂, Fig.1A): total length 44.0, carapace length 10.0, rostrum length 9.0, telson length 9.0. First pereiopod: ischium (i) = 2.6, merus (m) = 4.8, carpus (c)= 5.0, propodus (p) = 3.0, dactylus (d) = 1.5. Second pereiopod: i = 5, m = 5.8, c = 8.0, p = 9.0, d = 5.0. Third pereiopod: i = 3.5, m = 6.0, c = 3.0, p = 5.5, d = 2.0. Fourth pereiopod: i = 4.0, m = 6.2, c = 3.8, p = 7.5, d = 2.0. Fifth pereiopod: i = 4.0, m = 6.5, c = 4.0, p = 7.8, d = 2.8. ALLOTYPE (1♀ Fig.1B): total length 64.0, carapace length 16.0,rostrum length 12.0, telson length 10.0. First pereiopod: ischium (i) 4.0, merus (m) 7.0,carpus (c) 9.0, propodus (p) 4.5. dactylus (d) 2.5. Second pereiopod: i = 8.0, m = 9.0, c = 12.5, p = 13.5, d = 7.0. Third pereiopod: i = 3.8, m = 9.0, c = 3.8, p = 6.8, d = 2.5. Fourth pereiopod: i = 4.0, m = 9.0, c = 4.5, p = 8.5, d = 2.8. Fifth pereiopod: i = 4.0, m = 9.5, c = 4.8, p = 10.0, d = 3.0. PARATYPES: (based on 4 ♂) Total length 38–44, carapace length 9–10, rostrum length 8–14,telson length 6–9.5. First pereiopod: ischium (i) 2.0 –2.5; merus (m) 4.0–4.8, carpus (c) 6,0–7.5, propodus (p) 2.5–3.0; dactylus (d) 1.0–1.5. Second pereiopod: i = 4.5–5.0, m = 4.8–5.8, c = 7.2–8.0, p = 8.5–9.2, d = 4.75–5.0. Third pereiopod: i = 2.8–3.0, m = 5.5–6.0, c = 2.2–2.5, p = 4.5–5.5, d = 1.8–2.0. Fourth pereiopod: i = 3.0–3.5, m =5.0– 6.0, c = 2.5–3.0, p = 6.2–7.0, d = 1.5– 2.0. Fifth pereiopod: i = 3.5–3.8, m = 6.2–6.8, c = 3.75–4.5, p = 7.0–7.8, d = 2.0–2.8. (Based on 4 ♀) Total length 59.0–69.5, carapace length 16.0–18.0, rostrum length 11.5–14.0,telson length 8.5–10.0. First pereiopod: ischium (i) 4.5–4.8, merus (m) 6.8–7.0, carpus (c) 8.5–10.0, propodus (p) 4.25–5.0, dactylus (d)1.5–2.75. Second pereiopod: i = 6.75–8.0, m = 9.0–9.5, c = 12.0–14.0, p = 15.5–17.0, d = 7.5–8.2. Third pereiopod: i = 3.8–4.2, m = 8.0–10.0, c = 3.5–4.5, p = 7.0–8.0, d = 2.5–3.0. Fourth pereiopod: i = 4.0–4.5, m =9.0– 9.25, c = 4.0–4.5, p = 8.0–8.5, d = 2.5–3.0. Fifth pereiopod: i = 3.8–4.5, m = 9.0–10.0, c = 4.5–5.8, p = 9.5–10.0, d = 3.0–3.5. Description. Rostrum broad, overreaching antennal scale, tip directed slightly upwards. Rostral formula 9– 12/3–5 with 2 postorbitals; wide gap between 1 st and 2 nd post orbital tooth, 1 st post orbital and rest of the dorsals closely packed; 1 st ventral is located at half length of rostrum and last one at the level of 9/10 dorsal tooth. Carapace smooth, 6–8 mm in males, 17–19 mm in females; both antennal and hepatic spine present, latter situated below and behind the former (Fig.1C). Abdomen glabrous, pleurae of somites I–III typical, IV and V directed backwards, VI ending in spine. Telson broad, stout. conical with a median projection and two pairs of dorsal spines and two pairs of distal spines;1 st dorsal pair situated at 45–50%, 2 nd pair at 66–70% distance; inner pair of distal spines very long, overreaching tip of telson;3 pairs of plumose setae present between inner pair of spines. Eyes and cornea well developed, broader than eye stalk, slightly pigmented. Length of three segments of antennular peduncle, 5.5(proximal): 2(middle): 3(distal); lateral spine of basal segment not reaching middle segment. Tip of antennal scale round, outer spine subdistal, length 3 times as long as breadth. Mandible three segmented, middle segment shortest,apical one longest with one apical and one subapical row of setae (Fig.3F). Maxillula, maxilla,1 st maxilliped, 2 nd maxilliped typical of Macrobrachium. 3 rd maxilliped overreaching antennular peduncle, reaching nearly basal 1/3 rd of carpus of 1 st pereiopod.(Fig.2.a,b,c,d,e) 1 st pereiopod slender; chela overreaching antennal scale; ischium slightly shorter than propodus,0.61 to 0.66 times as long as merus,0.50 to 0.57 times as long as carpus; dactylus and palm equal (Fig.1D). 2 nd pereiopods exhibit sexual dimorphism. Male chelipeds equal,0.5 to 0.62 times of total body length; carpus longer than merus, ischum, shorter than propodus, podomere longest; dactylus equal or slightly longer than ischium; fingers distinctly longer than inflated palm with sharp ridge along the cutting edge (Fig.1E, 2 Ai,2D). Ratio (in %) of ischium, merus, carpus, propodus, dactylus, palm are 18(i):20.9(m):28.8(c):32.3(p):18(d):14.3(palm). Female chelipeds subequal, 0.59 to 0.63 times of body length (Fig.1F); carpus stout, conical near palm, longer than merus and ischium, shorter than propodus, podomere largest; dactylus equal to merus,0.50 to 0.62 times as long as propodus; palm inflated, equal to or longer than slender fingers,1 minute and 2 blunt denticles at the base of immovable finger and movable finger respectively. Ratio (in %) of ischium, merus, carpus, propodus, dactylus, palm are 16.0(i):22.5(m):29.7(c): [32.1(p)]:16.0(d): 15.4(palm). 3 rd to 5 th pereiopods simple, 5 th one longest. 1 st pleopod typical of Macrobrachium (Fig.1G). 2 nd pleopod in male with appendix masculina bearing 1 short, 2 long stiff distal setae and two lateral rows of 12-14 spinous setae (Fig.2C,2B), 2 nd pleopod in female simple.3 rd to 5 th pleopod simple in both the sexes (Fig.1I). Colouration. Body transluscent; Carapace, rostrum, antennal scale, antennular peduncle, first three abdominal pleurae without pigmentation, ventrolateral margin of 4 th,5 th, 6 th abdominal pleurae and uropod with dark brown pigmentation; 2 nd chelate leg has reddish brown pigmentation in entire carpus,outer margin of palm and fingers, half of merus close to carpus; red pigmentation in antennular flagella and at distal end of propodus; podomere joints of 3 rd,4 th & 5 th pereiopods with yellow bands.(Fig.2E). Discussion. A comparison of morphological characters (Table.2) shows that M. ramae sp. nov. shares several characters with M. gurudeve, M. jayasreei, M. kunjuramani and M. saengphani. However the new species can easily be distinguished from these species by the structure of rostrum, telson, appendix masculina and in presence of bigger proximal antennular peduncle segment as compared to middle and distal segments.A key is given below for distinctive identification of the five species. I dentification key: 1. Carapace shorter than rostrum........................................................................... 2 - Carapace longer than rostrum............................................................................ 3 2. Uropodal exopod with accessory spine; telson slender........................................................ 4 - Uropodal exopod without accessory spine;telson broad............................................... M.gurudeve 3. Uropodal exopod without accessory spine; telson slender.............................................. M.jayasreei - Uropodal exopod with accessory spine; telson broad............................................. M.ramae sp.nov. 4. Antennal spine with carina,males longer than females............................................ M.kunjuramani - Antennal spine without carina,males smaller than females........................................... M.saengphani Different haplotypes of M. ramae sp. nov. generated using both COI and 16S rRNA gene sequences of 3 males and 3 females cluster together in molecular phylogenetic trees, strongly suggests that the specimens belong to same species. Neither 16s rRNA nor COI gene sequences of M. gurudeve, M. jayasreei, M. kunjuramani are available in NCBI, except COI gene sequence of M. Saengphani, which forms a very distant clade from M. ramae sp. nov. (Fig. 4). Neighbor-joining tree of COI gene sequences of different Macrobrachium species shows that, M. ramae sp. nov. forms cluster with M. lamarrei and M. rude remains as separate clade. However, Neighbor-joining tree using 16S rRNA gene sequences shows that M. ramae sp. nov. forms a cluster with M. rude whereas M. lamarrei belongs to a separate clade. It is well established that morphologically M. lamarrei and M. rude are very easily distinguishable species and could be identified easily. M.rude differs hugely from M.ramae sp. nov. in having larger males than females measuring upto 130 mm of total length,2 nd cheliped 1.5 times longer than total body length.Moreover, all the sengments of 2 nd cheliped bear velvety pubescence, hence known as ‘hairy river prawn’. M. lamarrei also differs significantly from M.ramae sp. nov. in having longer rostrum with characteristic edentate gap, non-hairy appendix masculina longer than 2 nd pleopodal endopod and absence of subapical spine in uropodal exopod. If the sequences submitted to NCBI for M. lamarrei and M. rude are accurate in terms of species identification, then the sequences generated during the current study using COI and 16S rRNA genes should show similarity with any one of the species for both the gene fragments. This indicates that the samples for M. lamarrei and M. rude were collected and sequences were submitted without proper confirmation of the taxonomic status of those species, making their identification done rather doubtful. The sequences of M. lamarrei and M. rude retrieved from NCBI were submitted by three different research groups from two different countries. COI gene sequences MT483220 and MT483221, submitted as M. lamarrei were collected from Bhairab river, Bangladesh which is a coastal river carrying estuarine water. 16S rRNA sequences AY858836 and MG283139, submitted as M. rude were collected from Tamil Nadu and Orissa states of India respectively. These sequences rather indicate the presence of M. ramae sp. nov. in those locations and often be misidentified as other species of Macrobrachium and hence providing a hint of distribution of M. ramae sp. nov. spanning from coast of Bangladesh to entire East coast of India. Conclusion. The results of phylogenetic analysis have clearly pointed out that M. ramae sp. nov. is a new species as indicated through detail morphological study conducted during the present study. The results show the importance of both morphological and molecular data for accurate identification of any species and would surely help future taxonomists to figure out species level identification of the genus Macrobrachium in India with more clarity. Etymology. This new species is named in loving memory of the grandmother of the corresponding author (MD), late Rama Sengupta, who was a constant inspiration to her.The species name is a noun in the genitive singular.Published as part of Das, Mitali, Pahari, Priti Ranjan & Bhattacharya, Tanmay, 2021, A new species of palaemonid prawn Macrobrachium ramae sp. nov. (Malacostraca Decapoda: Palaemonidae) from Rupnarayana River, West Bengal, India with its molecular profiles, pp. 540-550 in Zootaxa 4952 (3) on pages 542-549, DOI: 10.11646/zootaxa.4952.3.6, http://zenodo.org/record/469064
Techniques for the Analysis and Understanding of Cosmic Evolution
No full textabstract: The Cosmic Microwave Background (CMB) has provided precise information on the evolution of the Universe and the current cosmological paradigm. The CMB has not yet provided definitive information on the origin and strength of any primordial magnetic fields or how they affect the presence of magnetic fields observed throughout the cosmos. This work outlines an alternative method to investigating and identifying the presence of cosmic magnetic fields. This method searches for Faraday Rotation (FR) and specifically uses polarized CMB photons as back-light. I find that current generation CMB experiments may be not sensitive enough to detect FR but next generation experiments should be able to make highly significant detections. Identifying FR with the CMB will provide information on the component of magnetic fields along the line of sight of observation.
The 21cm emission from the hyperfine splitting of neutral Hydrogen in the early universe is predicted to provide precise information about the formation and evolution of cosmic structure, complementing the wealth of knowledge gained from the CMB.
21cm cosmology is a relatively new field, and precise measurements of the Epoch of Reionization (EoR) have not yet been achieved. In this work I present 2σ upper limits on the power spectrum of 21cm fluctuations (Δ²(k)) probed at the cosmological wave number k from the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER) 64 element deployment. I find upper limits on Δ²(k) in the range 0.3 < k < 0.6 h/Mpc to be (650 mK)², (450 mK)², (390 mK)², (250 mK)², (280mK)², (250 mK)² at redshifts z = 10.87, 9.93, 8.91, 8.37, 8.13 and 7.48 respectively
Building on the power spectrum analysis, I identify a major limiting factor in detecting the 21cm power spectrum.
This work is concluded by outlining a metric to evaluate the predisposition of redshifted 21cm interferometers to foreground contamination in power spectrum estimation. This will help inform the construction of future arrays and enable high fidelity imaging and
cross-correlation analysis with other high redshift cosmic probes like the CMB and other upcoming all sky surveys. I find future
arrays with uniform (u,v) coverage and small spectral evolution of their response in the (u,v,f) cube can minimize foreground leakage while pursuing 21cm imaging.Dissertation/ThesisDoctoral Dissertation Physics 201
