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# The Temporary Exchange Problem

We formalize an allocation model under ordinal preferences that is more general than the well-studied Shapley-Scarf housing market. In our model, the agents do not just care which house or resource they get but also care about who gets their own resource. This assumption is especially important when considering temporary exchanges in which each resource is eventually returned to the owner. We show that several positive axiomatic and computational results that hold for housing markets do not extend to the more general setting. We then identify natural restrictions on the preferences of agents for which several positive results do hold. One of our central results is a general class of algorithms that return any allocation that is individually rational and Pareto optimal with respect to the responsive set extension.

• 54 publications
• 9 publications
04/30/2020

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## 1 Introduction

The Shapley-Scarf housing market is a well-studied formal model for barter markets where the goods can be dormitory rooms or kidneys [Sönmez and Ünver2011]. In the market, each agent owns a single good referred to as a house. The goal is to redistribute the houses to the agents in the most desirable fashion. ShSc74a ShSc74a showed that under strict preferences, a simple yet elegant mechanism called Gale’s Top Trading Cycle (TTC) is polynomial-time, strategyproof and find an allocation that is Pareto optimal and core stable. Even if the preferences are not strict, the algorithm can be suitably generalized while not losing any of the properties (see e.g., [Alcalde-Unzu and Molis2011, Aziz and de Keijzer2012, Saban and Sethuraman2013, Jaramillo and Manjunath2012]). There has also been work where agents have multi-unit demand and endowments [Sonoda et al.2014, Papai2007, Konishi et al.2001]. In this paper we focus on single-unit demands.

In the Shapley-Scarf market, agents only have preferences over houses. This is a reasonable assumption especially when the exchange is irrevocable. However, if the exchange is temporary, and the original house of an agent will be returned to her, the agent may care as to who temporarily used her house. In order to capture this additional issue, we consider the temporary exchange problem that is a generalisation of the Shapley-Scarf housing market. In this generalisation, an agent has preferences over outcomes that take into account both what house the agent gets and also who gets her own house. The assumption of the temporary exchange also makes sense when for example a kidney patient not only cares about getting a suitable kidney but also has preference over who should get his or her donor’s kidney. The setting also applies to reinsurance markets in which the identity of the insurers affects the preferences over arrangements. For this more general setting, we want to study fundamental questions as follows: does a core stable allocation exist and what is the complexity of finding it? What is the complexity of finding a Pareto optimal allocation?

#### Contributions

We formulate an exchange market setting that is more general than the well-studied Shapley-Scarf market. It models several scenarios where agents are performing a temporary exchange or they care about who gets their resource.

We first focus on core allocations in such settings and show that the core can be empty and it is NP-hard to check whether a core stable allocation exists. We also prove that finding a Pareto optimal allocation is NP-hard and testing Pareto optimality and weak Pareto optimality is coNP-complete.

We complement the computational hardness results by presenting succinct ILP and quadratic programming formulations for finding a Pareto optimal allocation. We then consider a weakening of Pareto optimality called Pareto optimality with respect to the responsive set extension. For this particular concept, we propose a general class of polynomial-time algorithms that return any allocation that is individually rational and Pareto optimal with respect to the responsive set extension.

We also consider strategic aspects and present two key impossibility results. Firstly, there exists no core-consistent and strategyproof mechanism. Secondly, there exists no individually rational, Pareto optimal, and strategyproof mechanism. We then identify restrictions on the preferences in particular house-predominant and tenant-predominant preferences under which we regain the positive axiomatic and computational results that hold for the Shapley-Scarf market.

## 2 Temporary Exchange Problem

An instance of Temporary Exchange Problem is a tuple

where

• is the set of agents.

• is the set of houses.

• Endowment function maps each agent to a house. Each agent owns exactly one house . We will denote by .

• is the preference profile that specifies for each agent , the weak order preference relation over .***Note that in the standard housing market, the preferences are simply over the set of houses. Our model allows for more complex preferences. The symbol denotes “prefer at least as much”, denotes “strictly more prefer”, and denotes indifference.

A feasible outcome for the setting is an allocation of the houses to the agents. An allocation is a one-to-one mapping from to . If is the allocation, we will denote by as the house agent gets. We will denote by the agent who gets house .

Each agent cares about the combination of two things: which house she gets and who gets her own house. We will refer to this combination as the outcome for the agent.

For an agent , the outcome represents the scenario where gets house and gives house to agent . For an agent , the outcome represents the situation where keeps her own house. The outcome represents the situation where swaps her house with . When we write that , it means that prefers outcome to .

Therefore for any allocations and , an agent compares them only from the point of view of what house she gets and who gets her house: Note that an agent will be interested in the outcome only if is it more preferred by her than . Otherwise agent would rather not be part of the exchange. Note that there could be multiple allocation for which the outcome for an agent is the same.

## 3 Properties of allocations and mechanisms

We consider the standard properties in market design: (i) Pareto optimality: there should be no allocation in which each agent is at least as happy and at least one agent is strictly happier (ii) individual rationality (IR): no agent should have an incentive to leave the allocation program (iii) strategyproofness: no agent should have an incentive to misreport her preferences; and (iv) core stability: an allocation should be such that no set of agents can form a coalition where they just exchange among themselves to get a better outcome than the the allocation. We define these properties as follows.

An allocation is Pareto optimal if there exists no other allocation such that for all and for some . An allocation is weakly Pareto optimal if there exists no other allocation such that for all .

An allocation is individually rational if .

A coalition blocks an allocation on if there exists an allocation on such that for all , it is the case that and . An allocation is core stable if it admits no blocking coalition.

A allocation algorithm is strategyproof if no agent can misreport and get a better outcome.

## 4 Core stability

We first show that unlike the Shapley-Scarf housing market, the Temporary Exchange market may not admit a core stable allocation.

###### Proposition 1

The core of a Temporary Exchange setting instance can be empty.

###### Proof.

Consider an instance where

• for all

• The preferences are as follows.

 1:(h2,2),(h0,0),(h1,1) 2:(h3,3),(h1,1),(h2,2) 3:(h4,4),(h2,2),(h3,3) 4:(h0,0),(h3,3),(h4,4) 0:(h1,1),(h4,4),(h0,0)

Our first claim is that for an allocation to be individually rational, it must be that an agent makes no exchange or she makes a pairwise exchange with agent or agent . An agent is only interested in outcomes or or . Suppose gets a house different than . Then she gets either or . Suppose that agent gets house . Then the outcome is only acceptable to only if gets house . Similarly, if agent gets house , then the outcome is only acceptable to only if gets house .

Now consider any individually rational allocation. From the claim established it follows that the allocation involves zero or more pairwise exchanges. Since there are an odd number of agents, at least one agent will not be part of any exchange. Let such as agent be

. Note that is interested to make an pairwise exchange with . Agent also prefers outcome over or . Hence agents in form a blocking coalition. ∎

Next, we show that it is NP-hard to check whether a core stable allocation exists. The proof uses the example in the proof of Proposition 1.

###### Proposition 2

Checking whether there exists a core stable allocation is NP-hard if there are indifferences in the preferences and even if each agent has at most 6 acceptable outcome pairs.

###### Proof.

We reduce from the following NP-complete problem.

Name: ExactCoverBy3Sets (X3C):
Instance: A pair , where is a set and is a collection of subsets of such that for some positive integer and for each and each element in appears three times in .
Question: Is there a sub-collection that is a partition of ?

For each integer , we have a corresponding gadget instance where ; ; for all The preferences are as follows.

 1j: (hj2,2j),(hj0,0j),(hj1,1j) 2j: (hj3,3j),(hj1,1j),(hj2,2j) 3j: (hj4,4j),(hj2,2j),(hj3,3j) 4j: (hj0,0j),(hj3,3j),(hj4,4j) 0j: {(e(0k),0i):{i,j,k}∈S},(hj1,1j),(hj4,4j),(hj0,0j)

Note that agent is interested to perform exchanges with other agents and from other gadgets.

The overall allocation instance involves agents and houses from all the gadgets so that and .

We claim that there exists a core stable allocation if and only if we have a yes instance of X3C. If we have a no instance of X3C, not every agent can form an exchange with other zero type agents so we have core deviation within gadget such as had in the proof of Proposition 1. Suppose we have a yes instance of X3C. In that case there is a partition of agents in who all get one of their most preferred outcomes. ∎

## 5 Pareto optimality

We now turn to the problem of finding Pareto optimal allocations.

### 5.1 Complexity of Pareto optimality

Since a Pareto optimal allocation is guaranteed to exist, we focus on computing such an allocation.

###### Proposition 3

Checking whether there exists an allocation that is most preferred for each agent is NP-complete if we allow indifferences in the preferences and even if each agent has at most 4 acceptable outcome pairs.Note that the problem is trivial if each agent has a unique most preferred outcome.

###### Proof.

We reduce from the following NP-complete problem.

Name: ExactCoverBy3Sets (X3C):
Instance: A pair , where is a set and is a collection of subsets of such that for some positive integer and for each and each element in appears three times in .
Question: Is there a sub-collection that is a partition of ?

Consider the setting instance in which ; ; for all . The preferences are as follows.

 j: {(e(k),i):{i,j,k}∈S},(j,hj)

Then there exists an allocation in which each agent gets a most preferred allocation if and only if there is a yes instance of X3C. ∎

###### Proposition 4

Finding a Pareto optimal allocation is NP-hard if there are indifferences in the preferences even if each agent has at most 4 acceptable outcome pairs.

###### Proof.

If there exists a polynomial-time algorithm to find a Pareto optimal allocation, then it will return an allocation that is most preferred for each agent if such an allocation exists. ∎

###### Proposition 5

Checking whether a given allocation is weakly Pareto optimal is coNP-complete even if preferences are strict and even if each agent has at most 4 acceptable outcome pairs.

###### Proof.

Use the same proof as the previous one but consider the endowment allocation. We can also make preferences strict. ∎

### 5.2 ILP and Quadratic programming formulations

Although computing a Pareto optimal allocation is NP-hard, one can still write an ILP to compute a maximum utility and hence Pareto optimal allocation. Since agents only express ordinal preferences, one can suppose that each agent has utility for receiving house and having a visitor in her own house .

 max∑i,j,k∈Nxi,j,k⋅wi,j,k
 xi,j,k∈{0,1} for i,j,k∈N, and
 xi,k,i=xi,i,k=xk,i,i=0 for i,k∈N,i≠k
 For fixed i∈N,∑j,k∈Nxi,j,k=1 for all j,k∈N,
 For fixed j∈N,∑i,k∈Nxi,j,k=1 for all i,k∈N,
 For fixed k∈N,∑i,j∈Nxi,j,k=1 for all i,j∈N,

where is a weighted value corresponding to the preference of agent , receiving house and a visitor in her own house .

One can also write a quadratic program that is even more compact.

#### Quadratic programming for maximum utility

 max∑i,j∈Nxi,j⋅wi,j,k⋅xj,k
 For fixed i∈N,∑j∈Nxi,j=1 for all j∈N
 For fixed j∈N,∑i∈Nxi,j=1 for all i∈N

### 5.3 Responsive extension preferences

In certain scenarios, an agent may have underlying preferences over houses and over tenants . Her preferences over the combinations of houses and tenants may depend naturally on their underlying preferences. In particular, we study the situation where the preferences are based on the responsive set extension. We consider the responsive set extension that is a subset of responsive preferences that only relates allocations when one allocation is unambiguously at least as preferred as another. We say that agent ’s preferences over are responsive if for any and ,

 (h≿Hih′)∧(j≿Nij′)⟺(h,j)≿RSi(h′,j′).

We say that allocation is RS-PO (Pareto optimal with respect to the responsive set extension) if there exists no other allocation such that for all and for some . Note that if an allocation is not RS-PO, it admits an unambiguous improvement for the agents.

We say that an allocation is RS-IR (individually rational with respect to the responsive set extension) if . Our main result in this section is that there exists a polynomial-time algorithm to compute an RS-IR and RS-PO allocation.

###### Proposition 6

There exists a polynomial-time algorithm that returns an individually rational and Pareto optimal allocation with respect to responsive set extension.

First we outline a new problem called RS-AA. In this problem an agent gets an acceptable allocation if it gets some tenant agent that is one of the acceptable agents and a house that is one of the acceptable houses.

###### Lemma 1

RS-AA can be solved in polynomial time.

###### Proof.

In the algorithm we first force symmetry in multiple ways. If an agent does not have as one of his acceptable tenants, then cannot be one of ’s acceptable houses and is removed from ’s list if does not have house as one of this acceptable houses, then is removed from ’s acceptable set of agents. After making the preferences symmetric in this way, we can simply check whether there is a perfect matching that matches each agent to one his acceptable houses. We argue why this sufficient.

We will frame the problem in a perfect matching context. Suppose there is a RS-AA problem with a set of agents and a set of houses . Every agent has two most preferred sets, , the preferred houses for the agent, and , the preferred tenants to their own house. A RS-AA solution requires that an agent is matched to a house owned by agent iff finds acceptable as a tenant and agent considers house acceptable. Hence the setup of a matching problem over the bipartite graph with vertices with edges existing iff agent prefers house and agent prefers tenant . Then a perfect matching on corresponds one-to-one with a solution of RS-AA. ∎

Lemma 1 is interesting because similar problems are NP-complete for several matching settings in which a match has three dimensions [Chan et al.2016, Huzhang et al.2017, Ng and Hirschberg1991]. We now show that the polynomial-time algorithm for RS-AA can be used as a sub-routine to compute an RS-IR and RS-PO allocation. In order to do so we present an adaptation and generalisation of the Preference Refinement Algorithm [Aziz et al.2013] that is defined for hedonic coalition formation and that requires complete preferences. For our problem we do not have complete preferences but each preference relation has multidimensional components—one involving a house and one involving a tenant agent.

###### Lemma 2

If RS-AA runs in polynomial time for any allocation problem, then a RS-Pareto-Optimal allocation can be computed in polynomial time.

###### Proof.

An oracle to solve RS-AA can be used to compute an RS-Pareto-Optimal and RS-IR allocation. The details are specified in Algorithm 1.

We first start with the agent’s actual preferences. An acceptable allocation indeed exists: one in which each agent stays where she is. We now start changing the agents’ preferences, one component preference of one agent at a time. For any given agent , we see whether an acceptable allocation still exists if the least preferred acceptable elements of the component preference are now unacceptable. If an allocation exists, in that case those elements are permanently marked as unacceptable and the algorithm proceeds. We do so until no agent’s preference can be modified. At this point, we know that a perfect allocation is Pareto optimal with respect to the responsive preferences. ∎

## 6 Incentives

Up till now we have assumed that agents act sincerely and report their truthful preferences. In this section, we explore scenarios where agents may misreport their preferences. We show that for the Temporary Exchange markets, strategyproofness is incompatible with other desirable axioms.

###### Proposition 7

There exists no individually rational, Pareto optimal, and strategyproof mechanism.

###### Proof.

Consider the following instance of the problem.

• for all

• The preferences are as follows.

 1: (h2,2),(h2,0),(h0,2),(h0,0),(h1,1) 2: (h3,1),(h3,3),(h1,1),(h1,3),(h2,2) 3: (h0,2),(h0,0),(h2,2),(h2,0),(h3,3) 0: (h1,3),(h1,1),(h3,3),(h3,1),(h0,0)

The only two individually rational allocations are and .

Allocation :

 1: (h2,2),(h2,0),(h0,2),(h0,0),(h1,1) 2: (h3,1),(h3,3),(h1,1),(h1,3),(h2,2) 3: (h0,2),(h0,0),(h2,2),(h2,0),(h3,3) 0: (h1,3),(h1,1),(h3,3),(h3,1),(h0,0)

Allocation :

 1: (h2,2),(h2,0),(h0,2),(h0,0),(h1,1) 2: (h3,1),(h3,3),(h1,1),(h1,3),(h2,2) 3: (h0,2),(h0,0),(h2,2),(h2,0),(h3,3) 0: (h1,3),(h1,1),(h3,3),(h3,1),(h0,0)

If the outcome under the original preferences is , then agent 2 can misreport as follows to obtain an outcome in bold which is the only Pareto optimal and individually rational allocation under the misreported preferences.

 1: (h2,2),(h2,0),(h0,2),(h0,0),(h1,1) 2: (h3,3),(h2,2) 3: (h0,2),(h0,0),(h2,2),(h2,0),(h3,3) 0: (h1,3),(h1,1),(h3,3),(h3,1),(h0,0)

In an individually rational allocation either gets outcome or . If gets outcome , then gets outcome or . If gets outcome , then the outcome is which is not Pareto optimal. If gets outcome , then gets outcome . Then gets outcome which implies that and can swap each others’ houses to get a Pareto improvement. Thus in an individually rational allocation, gets outcome . Hence gets outcome . By Pareto optimality, gets outcome and gets . Under the allocation in bold, gets outcome thereby violating strategyproofness.

We now suppose that the outcome of the original preferences is . If the outcome is , then 1 can misreport to obtain an outcomes or in bold which are the only Pareto optimal and individually rational allocations under the following preferences.

Allocation

 1: (h2,2),(h1,1) 2: (h3,1),(h3,3),(h1,1),(h1,3),(h2,2) 3: (h0,2),(h0,0),(h2,2),(h2,0),(h3,3) 0: (h1,3),(h1,1),(h3,3),(h3,1),(h0,0)

Allocation

 1: (h2,2),(h1,1) 2: (h3,1),(h3,3),(h1,1),(h1,3),(h2,2) 3: (h0,2),(h0,0),(h2,2),(h2,0),(h3,3) 0: (h1,3),(h1,1),(h3,3),(h3,1),(h0,0)

Allocation already provides a beneficial outcome for agent thereby violating strategyproofness. Suppose the outcome is allocation . In that case agent can misreport as follows to obtain the only Pareto optimal and individually rational allocation which provides an improvement for agent thereby violating strategyproofness.

 1: (h2,2),(h1,1) 2: (h3,1),(h3,3),(h1,1),(h1,3),(h2,2) 3: (h0,0),(h3,3) 0: (h1,3),(h1,1),(h3,3),(h3,1),(h0,0)

This concludes the proof.

We say that a mechanism is core-consistent if it returns a core stable allocation whenever a core stable allocation exists. The same argument can be used to prove that there exists no mechanism that is core-consistent and strategyproof.

###### Proposition 8

There exists no core-consistent and strategyproof mechanism.

In the subsequent sections, we show negative results from the previous sections can be circumvented if we consider special structure on the preferences.

## 7 Predominant Preferences

In this section, we consider preference restrictions under which we obtain positive axiomatic results.

### 7.1 House-predominant Preferences

A particularly restricted version of consistent preferences is in which agents have strict underlying preferences over the houses, care predominantly about the houses and use the preferences over agents as a tie-breaker. We will refer to these preferences as house-predominant preferences. The core is non-empty for these preferences. This follows from the fact that the TTC mechanism designed for basic housing markets works for our setting. We first describe the TTC mechanisms.

TTC: For a housing market with strict preferences, we first construct the corresponding directed graph where and is specified as follows: each house points to its owner and each agent points to the most preferred house in the graph. Then, we start from an agent and walk arbitrarily along the edges until a cycle is completed. This cycle is removed from . Within the removed cycle, each agent gets the house he was pointing to. The graph is adjusted so that the remaining agents point to the most preferred houses among the remaining houses. The same step is repeated until the graph is empty.

###### Proposition 9

For house-predominant preferences in which agents have strict preferences over houses, the TTC rule is core stable and Pareto optimal.

###### Proof.

We first argue for core stability. When any agent is removed from the graph along with his allocated house , then is a maximally preferred house for from among the remaining houses. Therefore cannot be in a blocking coalition with the agents remaining in the graph.

We now argue for Pareto optimality. Let be the th trading cycle that is removed from the trading cycle graph. In any allocation in which none of the agents are worse off than in the allocation produced by TTC, these agents must be allocated to houses in . Taking this as the base case, it follows by easy induction that in , the agents of must be allocated to houses in the th trading cycle. Next, suppose that is a agent in for some . Then no house in is more preferred by than the house that the TTC mechanism assigns him to. It follows that no agent is strictly better off in than in the allocation produced by TTC. ∎

###### Proposition 10

For house-predominant preferences in which agents have strict preferences over houses, the TTC rule is strategyproof.

The argument is similar to the strategyproof argument for TTC for the standard Shapley-Scarf market. An agent cannot get a better house by misreporting. Suppose the agent gets the same house but a different agent takes her house. But this is not possible by the specification of TTC because the agent gets the house she points to in a cycle.

### 7.2 Tenant-predominant Preferences

We can also turn around the problem completely so as to consider a setting in which agents have strict underlying preferences over other agents, care predominantly about the tenants and use the preferences over houses as a tie-breaker. We will refer to such preferences as “tenant-predominant preferences.”

TTTC: For a housing market with strict preferences, we first construct the corresponding directed graph where and is specified as follows: each agent points to its house and each house points to the agent most preferred by its owner. Then, we start from an agent and walk arbitrarily along the edges until a cycle is completed. This cycle is removed from . Within the removed cycle, each house it taken by the agent it was pointing to. The graph is adjusted so that the remaining houses point to the agent most preferred by its owner. The same step is repeated until the graph is empty.

The following propositions can be proved for TTTC and tenant-predominant preferences. The arguments for the propositions above are very similar to those of TTC for house-predominant preferences.

###### Proposition 11

For tenant-predominant preferences which agents have strict preferences over other agents, the TTTC mechanism is core stable and Pareto optimal.

###### Proposition 12

For tenant-predominant preferences which agents have strict preferences over other agents, the TTTC rule is strategyproof.

The same results also hold for “tenant-only preferences” in which agents have strict preferences over tenants and do not care about which house they get.

## 8 Conclusions

We considered a natural generalization of the Shapley-Scarf housing market with ordinal preferences. Several positive axiomatic and computational results that hold for the Shapley-Scarf housing market no longer hold for the temporary exchange market. On the other hand, we present some positive algorithmic and axiomatic results when preferences have more structure.

The problem can be extended in several ways. Typically when exchanging holiday homes, it may be the case that the exact duration of holidays may not coincide for the people in the market. An extended model would allow for time windows and having back to back bookings.

We presented an algorithm to compute an RS-PO allocation. One can also consider the core. A coalition RS-blocks an allocation on if there exists an allocation on such that for all , it is the case that and . An allocation is RS core stable if it admits no RS blocking coalition. If all preferences over houses are strict, then TTC returns an RS core stable outcome and if all preferences over agents are strict, then TTTC returns an RS core stable outcome. For weak preferences, the following problems appear to be interesting. Does an RS core stable allocation always exist? What is the complexity of computing such an allocation?

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text:
Dineen's Probability in Finance: A question on limiting behaviour of expectations of sequences of positive integrable random variables

In the above book (first edition), the author proves the following theorem:

If $(X_n)_{n=1}^{\infty}$ and $(Y_n)_{n=1}^{\infty}$ are increasing sequences of positive integrable random variables on the probability space $(\Omega, \mathcal{F},P)$ and if $$\lim_{n \to \infty} X_n = \lim_{n \to \infty} Y_n$$ almost surely, then $$\lim_{n\to\infty}\mathbb{E}\lbrack X_n\rbrack = \lim_{n\to\infty}\mathbb{E}\lbrack Y_n\rbrack.$$

In course of the proof, the author needs to prove, among other things, that $\lim_{n\to\infty} X_n(\omega) = \lim_{n\to\infty} X_{n}^{\lbrack j_n \rbrack}(\omega)$ for every $\omega \in \Omega,$ where $X^{\lbrack m \rbrack}$ denotes the $m-$th truncation of $X$ and $j_n$ is a certain previously defined strictly increasing ($j_{n+1} > j_n$) sequence of natural numbers. Here, he distinguishes two cases: 1) in case $\lim_{n\to\infty} X_{n}(\omega) < \infty,$ we have $X_{n}(\omega) < j_n$ for every $n$ bigger than certain $n_0$ so that we plainly have (due to the definition of $X^{m}(\omega)$) that $X_{n}^{\lbrack j_n \rbrack}(\omega) = X_n(\omega)$ for all $n \geq n_0.$ 2) In case $\lim_{n\to\infty} X_{n}(\omega) = \infty,$ he says:

for all $n,$ we have either $X_{n}(\omega) - X_{n}^{\lbrack j_n \rbrack}(\omega) \leq 1/2^{j_n}$ or $X_{n}^{\lbrack j_n \rbrack} = j_n.$ Since $j_n \geq n,$ we have, in either case, $\lim_{n \to \infty} X_n^{\lbrack j_n \rbrack} = \infty.$

This would clearly establish the claim that $\lim_{n\to\infty} X_n(\omega) = \lim_{n\to\infty} X_{n}^{\lbrack j_n \rbrack}(\omega)$ but I have a couple of questions here:

• First, from where does it follow that $$X_{n}(\omega) - X_{n}^{\lbrack j_n \rbrack}(\omega) \leq 1/2^{j_n}$$ and for what $n'$s is it true? My guess is that it has something to do with pointwise convergence of the truncations $X^{\lbrack m \rbrack}$ to $X$ for $m \to \infty$ (this seems obvious).
• Second, why is it not enough to say: if $\lim_{n \to \infty} X_n(\omega) = \infty,$ then $X_{n}^{\lbrack j_n \rbrack} = j_n$ for $n$ big enough and since $j_n \geq n,$ we have $\lim_{n\to \infty}X_{n}^{\lbrack j_n \rbrack} = \infty$ and we ar done (does it have sth in common with the fact that $j_n$ depends on $n$?)
• @Math1000: I am not saying the theorem is not rigorous, I just do not understand one tiny detail of its proof. This detail is somehow captured in my questions above. And yes, it uses truncations, if only implicitly: they are defined on p. 123 in the first edition. – Jorge.Squared Jul 25 '18 at 11:05
• @Math1000: maybe you are referring to a similar theorem dealing with positive bounded random variables only, whereas the theorem I am referring to deals with positive integrable RVs? – Jorge.Squared Jul 25 '18 at 11:26
• Ah, indeed I had the wrong theorem; the one I was looking at states "increasing sequences of simple positive random variables." I will delete my previous comments. – Math1000 Jul 25 '18 at 11:37
• In the proof of the (correct) theorem, the author still is not using the aforementioned truncations, but instead the "canonical sequence" of simple random variables $\{X_n\}$ defined explicitly such that $|X_n(\omega)-X(\omega)|\leqslant 2^{-n}$ for all $n$ and $\omega$. I suggest you study the construction of the $X_n$ carefully. – Math1000 Jul 25 '18 at 11:44
• @Math1000: Thank you, your response suggests that the second edition has a different proof. This raises the question whether the present "proof" is correct or not. I still wonder. – Jorge.Squared Jul 25 '18 at 11:52

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Please subscribe to the official Codeforces channel in Telegram via the link https://t.me/codeforces_official. ×

D. Arthur and Walls
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

Finally it is a day when Arthur has enough money for buying an apartment. He found a great option close to the center of the city with a nice price.

Plan of the apartment found by Arthur looks like a rectangle n × m consisting of squares of size 1 × 1. Each of those squares contains either a wall (such square is denoted by a symbol "*" on the plan) or a free space (such square is denoted on the plan by a symbol ".").

Room in an apartment is a maximal connected area consisting of free squares. Squares are considered adjacent if they share a common side.

The old Arthur dream is to live in an apartment where all rooms are rectangles. He asks you to calculate minimum number of walls you need to remove in order to achieve this goal. After removing a wall from a square it becomes a free square. While removing the walls it is possible that some rooms unite into a single one.

Input

The first line of the input contains two integers n, m (1 ≤ n, m ≤ 2000) denoting the size of the Arthur apartments.

Following n lines each contain m symbols — the plan of the apartment.

If the cell is denoted by a symbol "*" then it contains a wall.

If the cell is denoted by a symbol "." then it this cell is free from walls and also this cell is contained in some of the rooms.

Output

Output n rows each consisting of m symbols that show how the Arthur apartment plan should look like after deleting the minimum number of walls in order to make each room (maximum connected area free from walls) be a rectangle.

If there are several possible answers, output any of them.

Examples
Input
5 5.*.*.*****.*.*.*****.*.*.
Output
.*.*.*****.*.*.*****.*.*.
Input
6 7***.*.*..*.*.**.*.*.**.*.*.*..*...********
Output
***...*..*...*..*...*..*...*..*...********
Input
4 5............***..*..
Output
....................


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# Subharmonic function on a twice punctured complex plane

is the twice punctured complex plane parabolic or hyperbolic? In this sense: does $\mathbb{C}-\{0,1\}$ admit a nonconstant, negative, subharmonic function?

Thanks,

-

A subharmonic function which is bounded from above near a polar set automatically extends through it. Therefore, any negative subharmonic function on $\mathbb C \setminus\{0,1\}$ induces a negative subharmonic function on $\mathbb C$, and by Liouville theorem, it must be constant.
The $j$-invariant in the theory of elliptic curves is a covering map from the upper half plane to the complex plane punctured at $0$ and $1$. See Koblitz, Introduction to Elliptic Curves and Modular Forms.
I don't think you mean the $j$-invariant (which does take both values $0$ and $1$) but rather a modular function for $\Gamma_0(4)$. –  Dan Petersen Dec 19 '13 at 16:28


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# Singular Value in Machine Learning

I'm reading the paper (http://proceedings.mlr.press/v9/glorot10a/glorot10a.pdf) from Glorot and Bengio. There is something that I don't understand at the abstract section on page 1.

"Training may be more difficult when the singular values of the Jacobian associated with each layer are far from 1"

Why is the singular value of the Jacobian important for training?

Why is the singular value being far from 1 difficult for training?

Why? As a heuristic, imagine that all the singular values for each layer were 2, and you have $$n$$ layers. Then the singular values for the entire network would be $$2^n$$. So, if the singular values of the layers are larger than 1, the singular values for the entire network can grow exponentially in the number of layers. Similarly if they're less than 1, they can vanish exponentially fast.


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# Need script to copy specific .txt files

October 1, 2010 at 03:02:00
Specs: Windows XP, Pent.4 / 2 gig
 Hello,I need help writing script to copy 60+ 'specifically named' .txt files fromone folder to another. The farthest I've gotten is-copy "c:\fubar1\abc.txt" "c:\fubar2\abc.txt"That copies abc.txt, but putting def.txt after the abc.txt gives me "cannot find file"Thx

See More: Need script to copy specific .txt files

#1
October 1, 2010 at 21:20:08
 What are these specifically names files?Are there any similarities?----You might be able to stick it in a loop, and get it done in a line or two. Get back to me.Can I put a question here?

Report •

#2
October 2, 2010 at 19:14:20
 That's the problem. The only similarities are that they are .txt files. Wildcards are out of the question. Other than that, they have xxxxcv, xxxxfisc, xxxxinv. The xxxx are 60 plus differently named files.

Report •

#3
October 2, 2010 at 20:44:27
 copy *.txt c:\destination  GNU win32 packages | Gawk

Report •

Related Solutions

#4
October 3, 2010 at 18:22:32
 The problem with that ghostdog is what happens if there are more text files in the folder that he doesn't want moved?You might have to spend a bit of time and manually type them all in...COPY "P:\a\t\h\File1.txt+File2.txt+Fil..." "P:\a\t\h\"Can I put a question here?

Report •

#5
October 4, 2010 at 02:33:48
 I tried that, but nothing gets copied. Typing in all those .txt files is no problem. I just can't seem to find a 'command, argument, symbol' that allows me to string all those files in the specified folder.The only thing I saw that worked was replicating -----copy "c:\*\abc.txt" "c:\%\abc.txt"copy "c:\*\def.txt" "c:\%\def.txt"copy "c:\*\ghi.txt" "c:\%\ghi.txt"If that's the only way, so be it. Since I'm new to scripting, I thought there'd be a different way.

Report •

#6
October 4, 2010 at 12:33:51
 If you want to right all of the names of the files you want to move in a text file, you can use this:FOR /f %%a IN (FileName.txt) DO ( COPY "P:\a\t\h\%%a" "P:\a\t\h\%%a" )----C:\Users\Matt\Desktop>FOR /f %a IN (Names.txt) DO (COPY "Folder 1\%a" "Folder 2\ %a") C:\Users\Matt\Desktop>(COPY "Folder 1\123.txt" "Folder 2\123.txt" ) 1 file(s) copied. C:\Users\Matt\Desktop>(COPY "Folder 1\456.txt" "Folder 2\456.txt" ) 1 file(s) copied. C:\Users\Matt\Desktop>(COPY "Folder 1\789.txt" "Folder 2\789.txt" ) 1 file(s) copied. Can I put a question here?

Report •

#7
October 5, 2010 at 01:50:45
 Thanks so much! Here's the working script---@echo offcd C:\Users\Myself\Desktop\EOM\FOR %a IN (abc.txt def.txt ghi.txt) DO (COPY "C:\Users\Curtis\Desktop\EOM\%a" "C:\Users\Myself\Desktop\EOM2\%a")

Report •


text:
# Khovanov homology is a skew Howe 2-representation of categorified quantum slm

19.08.2013-20.08.2013

Organisiert von: A. Beliakova

Joint work with Aaron Lauda and David Rose (University of Southern California).

Khovanov homology, which categorifies the Jones polynomial, was first introduced in a mostly combinatorial fashion. However, the Jones polynomial has deep roots in the theory of representations of the quantum group slm. We show that similar links appear at the categorified level as well: the original combinatorics of cobordisms (or rather a foamy version of them due to Blanchet) can be understood in terms of higher representation theory. Specifically, we show that the combinatorially defined foam constructions of Khovanov homology arises as a family of 2-representations of categorified quantum slm. The heart of the process is given by categorified skew-Howe duality, due to Cautis-Kamnitzer-Licata, which drives to a very rich presentation of the Reshetikhin-Turaev invariants of knots.

The first talk will be devoted to review webs and skew-Howe duality, as well as the way the braiding can be understood in terms of a quantum Weyl group action, following Cautis, Kamnitzer, Licata and Morrison. The second lecture will focus on categorification of this phenomenon.

 Monday, 19.08.13 Zeit Referent Vortragstitel Raum 11:00 Hoel Queffelec(Pierre and Marie Curie University) Khovanov homology is a skew Howe 2-representation of categorified quantum slm Y27H28 Tuesday, 20.08.13 Zeit Referent Vortragstitel Raum 11:00 Hoel Queffelec(Pierre and Marie Curie University) Khovanov homology is a skew Howe 2-representation of categorified quantum slm Y27H28


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## Gauss-Kronrod quadrature formulae - A survey of fifty years of research

Sotirios E. Notaris

### Abstract

Kronrod in 1964, trying to estimate economically the error of the $n$-point Gauss quadrature formula for the Legendre weight function, developed a new formula by adding to the $n$ Gauss nodes $n+1$ new ones, which are determined, together with all weights, such that the new formula has maximum degree of exactness. It turns out that the new nodes are zeros of a polynomial orthogonal with respect to a variable-sign weight function, considered by Stieltjes in 1894, without though making any reference to quadrature. We survey the considerable research work that has been emerged on this subject, during the past fifty years, after Kronrod's original idea.

Full Text (PDF) [440 KB], BibTeX

65D32, 33C45

### Links to the cited ETNA articles

 [2] Vol. 9 (1999), pp. 26-38 G. S. Ammar, D. Calvetti, and L. Reichel: Computation of Gauss-Kronrod quadrature rules with non-positive weights [35] Vol. 41 (2014), pp. 1-12 Aleksandar S. Cvetković and Miodrag M. Spalević: Estimating the error of Gauss-Turán quadrature formulas using their extensions [83] Vol. 9 (1999), pp. 65-76 Walter Gautschi: Orthogonal polynomials and quadrature [87] Vol. 25 (2006), pp. 129-137 Walter Gautschi: The circle theorem and related theorems for Gauss-type quadrature rules [129] Vol. 28 (2007-2008), pp. 168-173 Dirk Laurie: Variable-precision arithmetic considered perilous - a detective story


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Enter the total revenue ($) and the expenses ($) into the Return on Revenue Calculator. The calculator will evaluate and display the Return on Revenue.

## Return on Revenue Formula

The following formula is used to calculate the Return on Revenue.

ROR = (TR-E) / TR * 100

• Where ROR is the Return on Revenue (%)
• TR is the total revenue ($) • E is the expenses ($)

## How to Calculate Return on Revenue?

The following example problems outline how to calculate Return on Revenue.

Example Problem #1:

1. First, determine the total revenue ($). • The total revenue ($) is given as: 750.
2. Next, determine the expenses ($). • The expenses ($) is provided as: 500.
3. Finally, calculate the Return on Revenue using the equation above:

ROR = (TR-E) / TR * 100

The values given above are inserted into the equation below and the solution is calculated:

ROR = (750-500) / 750 * 100 = 33.33 (%)

Example Problem #2:

For this problem, the variables needed are provided below:

total revenue ($) = 185 expenses ($) = 123

This example problem is a test of your knowledge on the subject. Use the calculator above to check your answer.

ROR = (TR-E) / TR * 100 = ?


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## Truth Tables and De Morgan's Rules

Read this chapter, which discusses Boolean variables as used in decision tables. Truth tables are used to collect variables and their values relative to decisions that have to be made within control structures.

### 9. Equivalent Boolean Expressions

Answer:speed > 2000(speed <= 2000)!(speed <= 2000)FTFTFT

# Equivalent Boolean Expressions

The original program fragment used this boolean expression

!(speed > 2000 && memory > 512)

which is explained in the following truth table (repeated from a previous page):

speed > 2000
memory > 512
speed > 2000 && memory > 512
!(speed > 2000 && memory > 512)
F
F
F
T
F
T
F
T
T
F
F
T
T
T
T
F

An equivalent program fragment used this boolean expression

speed <= 2000 || memory <= 512

which is explained in the following truth table:

speed > 2000
memory > 512
speed <= 2000
memory <= 512
speed <= 2000 || memory <= 512
F
F
T
T
T
F
T
T
F
T
T
F
F
T
T
T
T
F
F
F

Each table has the same first two columns. The true/false values in the last column of each table are the same, which shows that the two boolean expressions are equivalent. One expression can be used in place of the other in a program.

Question 9:Is there only one correct way to write an if statement in a program?


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### SLA_AOP

Apparent to Observed

ACTION:
Apparent to observed place, for sources distant from the solar system.
CALL:
CALL sla_AOP (RAP, DAP, DATE, DUT, ELONGM, PHIM, HM, XP, YP, TDK, PMB, RH, WL, TLR, AOB, ZOB, HOB, DOB, ROB)
##### GIVEN:
 RAP,DAP D geocentric apparent $\left[\phantom{\rule{0.3em}{0ex}}\alpha ,\delta \phantom{\rule{0.3em}{0ex}}\right]$ (radians) DATE D UTC date/time (Modified Julian Date, JD$-$2400000.5) DUT D $\Delta$UT: UT1$-$UTC (UTC seconds) ELONGM D observer’s mean longitude (radians, east +ve) PHIM D observer’s mean geodetic latitude (radians) HM D observer’s height above sea level (metres) XP,YP D polar motion $\left[\phantom{\rule{0.3em}{0ex}}x,y\phantom{\rule{0.3em}{0ex}}\right]$ coordinates (radians) TDK D local ambient temperature (K; std=273.15D0) PMB D local atmospheric pressure (mb; std=1013.25D0) RH D local relative humidity (in the range 0D0 – 1D0) WL D effective wavelength ($\mu m$, e.g. 0.55D0) TLR D tropospheric lapse rate (K per metre, e.g. 0.0065D0)

##### RETURNED:
 AOB D observed azimuth (radians: N=0, E=$9{0}^{\circ }$) ZOB D observed zenith distance (radians) HOB D observed Hour Angle (radians) DOB D observed $\delta$ (radians) ROB D observed $\alpha$ (radians)

NOTES:
(1)
This routine returns zenith distance rather than elevation in order to reflect the fact that no allowance is made for depression of the horizon.
(2)
The accuracy of the result is limited by the corrections for refraction. Providing the meteorological parameters are known accurately and there are no gross local effects, the predicted azimuth and elevation should be within about ′′01 for $\zeta <7{0}^{\circ }$. Even at a topocentric zenith distance of $9{0}^{\circ }$, the accuracy in elevation should be better than 1 arcminute; useful results are available for a further ${3}^{\circ }$, beyond which the sla_REFRO routine returns a fixed value of the refraction. The complementary routines sla_AOP (or sla_AOPQK) and sla_OAP (or sla_OAPQK) are self-consistent to better than 1 microarcsecond all over the celestial sphere.
(3)
It is advisable to take great care with units, as even unlikely values of the input parameters are accepted and processed in accordance with the models used.
(4)
Apparent $\left[\phantom{\rule{0.3em}{0ex}}\alpha ,\delta \phantom{\rule{0.3em}{0ex}}\right]$ means the geocentric apparent right ascension and declination, which is obtained from a catalogue mean place by allowing for space motion, parallax, the Sun’s gravitational lens effect, annual aberration, and precession-nutation. For star positions in the FK5 system (i.e. J2000), these effects can be applied by means of the sla_MAP etc. routines. Starting from other mean place systems, additional transformations will be needed; for example, FK4 (i.e. B1950) mean places would first have to be converted to FK5, which can be done with the sla_FK425 etc. routines.
(5)
Observed $\left[\phantom{\rule{0.3em}{0ex}}Az,El\phantom{\rule{1em}{0ex}}\right]$ means the position that would be seen by a perfect theodolite located at the observer. This is obtained from the geocentric apparent $\left[\phantom{\rule{0.3em}{0ex}}\alpha ,\delta \phantom{\rule{0.3em}{0ex}}\right]$ by allowing for Earth orientation and diurnal aberration, rotating from equator to horizon coordinates, and then adjusting for refraction. The $\left[\phantom{\rule{0.3em}{0ex}}h,\delta \phantom{\rule{0.3em}{0ex}}\right]$ is obtained by rotating back into equatorial coordinates, using the geodetic latitude corrected for polar motion, and is the position that would be seen by a perfect equatorial located at the observer and with its polar axis aligned to the Earth’s axis of rotation (n.b. not to the refracted pole). Finally, the $\alpha$ is obtained by subtracting the h from the local apparent ST.
(6)
To predict the required setting of a real telescope, the observed place produced by this routine would have to be adjusted for the tilt of the azimuth or polar axis of the mounting (with appropriate corrections for mount flexures), for non-perpendicularity between the mounting axes, for the position of the rotator axis and the pointing axis relative to it, for tube flexure, for gear and encoder errors, and finally for encoder zero points. Some telescopes would, of course, exhibit other properties which would need to be accounted for at the appropriate point in the sequence.
(7)
This routine takes time to execute, due mainly to the rigorous integration used to evaluate the refraction. For processing multiple stars for one location and time, call sla_AOPPA once followed by one call per star to sla_AOPQK. Where a range of times within a limited period of a few hours is involved, and the highest precision is not required, call sla_AOPPA once, followed by a call to sla_AOPPAT each time the time changes, followed by one call per star to sla_AOPQK.
(8)
The DATE argument is UTC expressed as an MJD. This is, strictly speaking, wrong, because of leap seconds. However, as long as the $\Delta$UT and the UTC are consistent there are no difficulties, except during a leap second. In this case, the start of the 61st second of the final minute should begin a new MJD day and the old pre-leap $\Delta$UT should continue to be used. As the 61st second completes, the MJD should revert to the start of the day as, simultaneously, the $\Delta$UT changes by one second to its post-leap new value.
(9)
The $\Delta$UT (UT1$-$UTC) is tabulated in IERS circulars and elsewhere. It increases by exactly one second at the end of each UTC leap second, introduced in order to keep $\Delta$UT within $±$$0$$s$$\phantom{\rule{-3.28502pt}{0ex}}.9$.
(10)
IMPORTANT – TAKE CARE WITH THE LONGITUDE SIGN CONVENTION. The longitude required by the present routine is east-positive, in accordance with geographical convention (and right-handed). In particular, note that the longitudes returned by the sla_OBS routine are west-positive (as in the Astronomical Almanac before 1984) and must be reversed in sign before use in the present routine.
(11)
The polar coordinates XP,YP can be obtained from IERS circulars and equivalent publications. The maximum amplitude is about ′′03. If XP,YP values are unavailable, use XP=YP=0D0. See page B60 of the 1988 Astronomical Almanac for a definition of the two angles.
(12)
The height above sea level of the observing station, HM, can be obtained from the Astronomical Almanac (Section J in the 1988 edition), or via the routine sla_OBS. If P, the pressure in millibars, is available, an adequate estimate of HM can be obtained from the following expression:

HM=-29.3D0*TSL*LOG(P/1013.25D0)

where TSL is the approximate sea-level air temperature in K (see Astrophysical Quantities, C.W.Allen, 3rd edition, §52). Similarly, if the pressure P is not known, it can be estimated from the height of the observing station, HM as follows:

P=1013.25D0*EXP(-HM/(29.3D0*TSL))

Note, however, that the refraction is nearly proportional to the pressure and that an accurate P value is important for precise work.

(13)
The azimuths etc. used by the present routine are with respect to the celestial pole. Corrections to the terrestrial pole can be computed using sla_POLMO.


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# Concepts behind fixed/random effects models

1. Can someone help me to understand fixed/random effect models? You may either explain in your own way if you have digested these concepts or direct me to the resource (book, notes, website) with specific address (page number, chapter etc) so that I can learn them without any confusion.
2. Is this true: "We have fixed effects in general and random effects are specific cases"? I would especially be grateful to get help where the description goes from general models to specific ones with fixed and random effects

This seems a great question as it touches a nomenclature issue in econometrics that disturbs students when switching to statistic literature (books, teachers, etc). I suggest you http://www.amazon.com/Econometric-Analysis-Cross-Section-Panel/dp/0262232197 chapter 10.

Assume that your variable of interest $y_{it}$ is observed in two dimensions (e.g. individuals and time) depends on observed characteristics $x_{it}$ and unobserved ones $u_{it}$. If $y_{it}$ are observed wages then we may argue that it's determined by observed (education) and unobserved skills (talents, etc.). But it's clear that unobserved skills may be correlated with educational levels. So that leads to the error decomposition: $u_{it} = e_{it}+v_i$ where $v_i$ is the error (random) component that we may assume to be correlated with the $x$'s. i.e. $v_i$ models the individual's unobserved skills as a random individual component.

Thus the model becomes:

$y_{it} = \sum_j\theta_jx_j + e_{it}+ v_{i}$

This model is usually labeled as a FE model, but as Wooldridge argues it would be wiser to call it a RE model with correlated error component whereas if $v_i$ is not correlated to the $x's$ it becomes a RE model. So this answer your second question, the FE setup is more general as it allows for correlation between $v_i$ and the $x's$.

Older books in econometrics tend to refer to FE to a model with individual specific constants, unfortunately this is still present in nowadays literature (I guess that in statistics they never have had this confussion. I definitevely suggest the Wooldridge lectures that develops the potential missunderstanding issue)

• Thanks for link to (1) Excellent Resource and (2) nice explanation – Stat-R Aug 10 '12 at 12:33
• This is a different way of explaining these ideas than I'm used to seeing, but really nicely done. +1 – gung Aug 11 '12 at 3:53

My best example of a random effect in a model comes from clinical trial studies. In clinical trial we enroll patients from various hospitals (called sites). The sites are selected from a large set of potential sites. There can be site related factors that effect the response to treatment. So in a linear model you often would want include site as a main effect.

But is it appropriate to have site as a fixed effect? We generally don't do that. We can often think of the sites that we selected for the trial as a random sample from the potential sites we could have selected. This may not be quite the case but it may be a more reasonable assumption than assuming the site effect is fixed. So treating site as a random effect allows us to incorporate the variability in the site effect that is due to picking a set of k sites out of a population containing N sites.

The general idea is that the group is not fixed but was selected from a larger population and other choices for the group were possible and would have led to different results. So treating it as a random effect incorporates that type of variability into the model that you would not get from a fixed effect.

• @ocram reference is quite interesting. It points out the heterogeneity regarding the FE definitions. But, to which definition is Stat-R refering to ? His second questions suggests that FE is considered as a RE with correlated random component. Under that definition and within your example, a FE would mean that a treatment could be correlated with an unobserved (or omiited) site effect, right? – JDav Aug 9 '12 at 22:52
• Nice - your last paragraph is a very succinct way of putting it. +1 – Luke Mar 22 '13 at 15:25
• @MichaelChernick: nice example. So you argue that hospital site should be treated as a random and not as a fixed effect. But what would be the actual difference in the outcome between these two options? If we treat it as fixed, then we will get a regression coefficient for each hospital, and can test e.g. if the main effect of hospital is significant. If we treat is a random, we will not get a regression coeff for each hospital (correct?); can we still test the main effect of hospital? More importantly, does it maybe increase/decrease power of other main effects/interactions in the model? – amoeba Feb 26 '14 at 23:10
1. Not sure about a book but here is an example. Suppose we have a sample of birth weights from a large cohort of babies over a long period of time. The weights of babies born to the same women would be more similar than the weights of babies born to different mothers. Boys are also heavier than girls.

So, a fixed effects model ignoring correlation in weights among babies born to the same mother is:

Model 1. mean birth weight = intercept + sex

Another fixed effects model adjusting for such correlation is:

Model 2. mean birth weight = intercept + sex + mother_id

However, firstly we might not be interested in the effects for each particular mother. Also, we consider the mother to be a random mother from the population all mothers. So we construct a mixed model with a fixed effect for sex and a random effect (i.e. a random intercept) for the mother:

Model 3: mean birth weight = intercept + sex + u

This u will be different for each mother, just as in Model 2 but it is not actually estimated. Rather, only its variance is estimated. This variance estimate gives us an idea as to the level of clustering of weights by mother.

Hope that makes some sense.


text:
# Math Help - continuous - differentiable question

1. ## continuous - differentiable question

is this true?
lets say that f and g are continuous on [a, b] and differentiable on (a, b).
If f'(x)=g'(x) for all x in (a, b), then f and g differ by a constant.

i think it false..

2. let $h(x)=f(x)-g(x),$ and $h'(x)=f'(x)-g'(x)=0,$ thus $h(x)$ is constant and the conclusion follows.

3. Why you think it is false?

If f'(x)=g'(x) then both functions have at x the same slope. For example x=1.

f'(1) = 3 then g'(x) = 3 --> this tells you that both graphs have a slope of 3 at x=3
but the funtion itself can be different. Like f(1) = 2 and g(1) = 4, then the two curves would have the same slope at x=1 but are lying parallel to each other.

The same for an maximum or minimum point. If f(1)=0 and g(1) =0 then both functions have an max or min at x=1 but the maximum/minimum value of f(x)could be at (1,3) and the other of g(x) could be at (1,4)

The function values I used are just random examples.

Thats how I understood it. Hope it helps.


text:
[1]:

import numpy as np
import matplotlib.pyplot as plt
from gpaw import GPAW
from abtem.dft import GPAWPotential
from abtem import *

---------------------------------------------------------------------------
ModuleNotFoundError                       Traceback (most recent call last)
<ipython-input-1-e1b472452493> in <module>
1 import numpy as np
2 import matplotlib.pyplot as plt
----> 3 from gpaw import GPAW
4 from abtem.dft import GPAWPotential

ModuleNotFoundError: No module named 'gpaw'

# ab initio potentials with GPAW¶

The independent atom model (IAM) neglects any effects due to bonding and charge transfer. However, since the nucleus and core electrons constitute most of the charge in an atom, this is often a good approximation. Nonetheless, the difference between the IAM and a more realistic model including the effects of bonding is measurable, at least in certain systems. This difference can obviously be important, since it contains all the chemistry of the system.

Here we go beyond the independent atom model using density functional theory (DFT). Note that you need a working GPAW installation for this tutorial, see the GPAW documentation for more information.

## DFT calculation¶

The first step for creating a DFT potential is to converge a DFT calculation.

The unit cell for the DFT calculation does not have to be orthogonal, but the potential has to be made orthogonal before the multislice simulation. Only unit cells that can be thought of as an extruded parallelogram are allowed. If standardize_cell raises an error, abTEM is unable to use the DFT calculation.

We will use the minimal hexagonal cell for our graphene DFT calculation.

[14]:

atoms = read('data/hexagonal_graphene.cif')

To run the DFT calculation, we use the GPAW calculator object. We set its real-space grid spacing to a small value of 0.1 Å and use a k-point grid of (3,3,1). The DFT real-space grid does not have to match the grid used in the multislice simulations.

Running the method .get_potential_energy triggers the DFT self-consistent field cycle to run, resulting in the GPAW object now containing the converged PAW electron density.

[15]:

gpaw = GPAW(h=.1, txt=None, kpts=(3,3,1))
atoms.calc = gpaw
atoms.get_potential_energy()

[15]:

-19.68456129990072

DFT calculations can be extremely computationally intensive, and may require massive parallelization. Running such simulations in a notebook is generally not recommended, hence, running the DFT calculation separately, and importing the GPAW calculator for the image simulation is typically a better workflow.

The GPAW object can be written to and read from disk as follows (here supressing GPAW text output on read).

[16]:

gpaw.write('data/graphene.gpw')

[17]:

gpaw = GPAW('data/graphene.gpw', txt=None)

## Using the GPAW potential in abTEM¶

It is straightforward to calculate a DFT potential from a converged GPAW calculation. The GPAWPotential object just requires a converged GPAW calculator (containing also the atoms) instead of an Atoms object. Note that we can use a finer sampling than was used for the computational grid.

[18]:

dft_pot = GPAWPotential(gpaw, sampling=.02)

The .build method converts the GPAWPotential to an ArrayPotential, representing the potential as a numpy array. This may be used in image simulations exactly the same way a potential derived from the IAM is used. Here we tile the potential by (3x2) in the $$xy$$ plane to visualize a larger field of view.

[19]:

dft_array = dft_pot.build()

dft_potential = dft_array.tile((3,2))

## Comparing DFT to IAM¶

[20]:

from abtem.structures import orthogonalize_cell
atoms = orthogonalize_cell(gpaw.atoms) * (3,2,1)

iam_potential = Potential(atoms, gpts=dft_potential.gpts, device='cpu').build()

Note that the zero level of the potential is set to 0 for both the IAM and DFT potentials to facilitate comparison. This makes their calculated relative difference diverge near the atom cores, which is here accounted for by setting diverging values to nan and coloring them with grey.

[21]:

projected_iam = iam_potential.array.sum(0)
projected_iam -= projected_iam.min()

projected_dft = dft_potential.array.sum(0)
projected_dft -= projected_dft.min()

absolute_difference = projected_iam - projected_dft

valid = np.abs(projected_iam) > 1
relative_difference = np.zeros_like(projected_iam)
relative_difference[:] = np.nan
relative_difference[valid] = 100*(projected_iam[valid] - projected_dft[valid]) / projected_iam[valid]

[22]:

fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(16, 4))

extent = [0, dft_potential.extent[0], 0, dft_potential.extent[1]]

im1 = ax1.imshow(projected_dft.T, cmap='cividis', vmax=300, extent=extent)
im2 = ax2.imshow(absolute_difference.T, vmin=-15, vmax=15, cmap='seismic', extent=extent)
im3 = ax3.imshow(relative_difference.T, vmin=-40, vmax=40, cmap='seismic', extent=extent)

labels = ('Projected potential [eV / e Å]', 'Absolute difference [eV / e Å]', 'Relative difference [%]')

for ax, im, label in zip((ax1, ax2, ax3), (im1, im2, im3), labels):
ax.set_xlabel('x [Å]')
ax.set_ylabel('y [Å]')

fig.colorbar(im, ax=ax, label=label)


text:
# $$p$$-Adic Base Leaves¶

Implementations of $$\mathbb{Z}_p$$ and $$\mathbb{Q}_p$$

AUTHORS:

• David Roe
• Genya Zaytman: documentation
• David Harvey: doctests

EXAMPLES:

$$p$$-Adic rings and fields are examples of inexact structures, as the reals are. That means that elements cannot generally be stored exactly: to do so would take an infinite amount of storage. Instead, we store an approximation to the elements with varying precision.

There are two types of precision for a $$p$$-adic element. The first is relative precision, which gives the number of known $$p$$-adic digits:

sage: R = Qp(5, 20, 'capped-rel', 'series'); a = R(675); a
2*5^2 + 5^4 + O(5^22)
sage: a.precision_relative()
20

The second type of precision is absolute precision, which gives the power of $$p$$ that this element is stored modulo:

sage: a.precision_absolute()
22

The number of times that $$p$$ divides the element is called the valuation, and can be accessed with the functions valuation() and ordp():

sage: a.valuation() 2

The following relationship holds:

self.valuation() + self.precision_relative() == self.precision_absolute().

sage: a.valuation() + a.precision_relative() == a.precision_absolute() True

In the capped relative case, the relative precision of an element is restricted to be at most a certain value, specified at the creation of the field. Individual elements also store their own precision, so the effect of various arithmetic operations on precision is tracked. When you cast an exact element into a capped relative field, it truncates it to the precision cap of the field.:

sage: R = Qp(5, 5); a = R(4006); a
1 + 5 + 2*5^3 + 5^4 + O(5^5)
sage: b = R(17/3); b
4 + 2*5 + 3*5^2 + 5^3 + 3*5^4 + O(5^5)
sage: c = R(4025); c
5^2 + 2*5^3 + 5^4 + 5^5 + O(5^7)
sage: a + b
4*5 + 3*5^2 + 3*5^3 + 4*5^4 + O(5^5)
sage: a + b + c
4*5 + 4*5^2 + 5^4 + O(5^5)

sage: R = Zp(5, 5, 'capped-rel', 'series'); a = R(4006); a
1 + 5 + 2*5^3 + 5^4 + O(5^5)
sage: b = R(17/3); b
4 + 2*5 + 3*5^2 + 5^3 + 3*5^4 + O(5^5)
sage: c = R(4025); c
5^2 + 2*5^3 + 5^4 + 5^5 + O(5^7)
sage: a + b
4*5 + 3*5^2 + 3*5^3 + 4*5^4 + O(5^5)
sage: a + b + c
4*5 + 4*5^2 + 5^4 + O(5^5)

In the capped absolute type, instead of having a cap on the relative precision of an element there is instead a cap on the absolute precision. Elements still store their own precisions, and as with the capped relative case, exact elements are truncated when cast into the ring.:

sage: R = ZpCA(5, 5); a = R(4005); a
5 + 2*5^3 + 5^4 + O(5^5)
sage: b = R(4025); b
5^2 + 2*5^3 + 5^4 + O(5^5)
sage: a * b
5^3 + 2*5^4 + O(5^5)
sage: (a * b) // 5^3
1 + 2*5 + O(5^2)
sage: type((a * b) // 5^3)
sage: (a * b) / 5^3
1 + 2*5 + O(5^2)
sage: type((a * b) / 5^3)

The fixed modulus type is the leanest of the p-adic rings: it is basically just a wrapper around $$\mathbb{Z} / p^n \mathbb{Z}$$ providing a unified interface with the rest of the $$p$$-adics. This is the type you should use if your primary interest is in speed (though it’s not all that much faster than other $$p$$-adic types). It does not track precision of elements.:

sage: R = ZpFM(5, 5); a = R(4005); a
5 + 2*5^3 + 5^4 + O(5^5)
sage: a // 5
1 + 2*5^2 + 5^3 + O(5^5)

$$p$$-Adic rings and fields should be created using the creation functions Zp and Qp as above. This will ensure that there is only one instance of $$\mathbb{Z}_p$$ and $$\mathbb{Q}_p$$ of a given type, $$p$$, print mode and precision. It also saves typing very long class names.:

sage: Qp(17,10)
17-adic Field with capped relative precision 10
sage: R = Qp(7, prec = 20, print_mode = 'val-unit'); S = Qp(7, prec = 20, print_mode = 'val-unit'); R is S
True
sage: Qp(2)
2-adic Field with capped relative precision 20

Once one has a $$p$$-Adic ring or field, one can cast elements into it in the standard way. Integers, ints, longs, Rationals, other $$p$$-Adic types, pari $$p$$-adics and elements of $$\mathbb{Z} / p^n \mathbb{Z}$$ can all be cast into a $$p$$-Adic field.:

sage: R = Qp(5, 5, 'capped-rel','series'); a = R(16); a
1 + 3*5 + O(5^5)
sage: b = R(23/15); b
5^-1 + 3 + 3*5 + 5^2 + 3*5^3 + O(5^4)
sage: S = Zp(5, 5, 'fixed-mod','val-unit'); c = S(Mod(75,125)); c
5^2 * 3 + O(5^5)
sage: R(c)
3*5^2 + O(5^5)

In the previous example, since fixed-mod elements don’t keep track of their precision, we assume that it has the full precision of the ring. This is why you have to cast manually here.

While you can cast explicitly as above, the chains of automatic coercion are more restricted. As always in Sage, the following arrows are transitive and the diagram is commutative.:

int -> long -> Integer -> Zp capped-rel -> Zp capped_abs -> IntegerMod
Integer -> Zp fixed-mod -> IntegerMod
Integer -> Zp capped-abs -> Qp capped-rel

In addition, there are arrows within each type. For capped relative and capped absolute rings and fields, these arrows go from lower precision cap to higher precision cap. This works since elements track their own precision: choosing the parent with higher precision cap means that precision is less likely to be truncated unnecessarily. For fixed modulus parents, the arrow goes from higher precision cap to lower. The fact that elements do not track precision necessitates this choice in order to not produce incorrect results.

TESTS:

sage: R = Qp(5, 15, print_mode='bars', print_sep='&')
sage: repr(R(2777))[3:]
'4&2&1&0&2'
sage: TestSuite(R).run()

sage: R = Zp(5, 15, print_mode='bars', print_sep='&')
sage: repr(R(2777))[3:]
'4&2&1&0&2'
sage: TestSuite(R).run()

sage: R = ZpCA(5, 15, print_mode='bars', print_sep='&')
sage: repr(R(2777))[3:]
'4&2&1&0&2'
sage: TestSuite(R).run()

An implementation of $$p$$-adic fields with capped relative precision.

EXAMPLES:

sage: K = Qp(17, 1000000) #indirect doctest
sage: K = Qp(101) #indirect doctest

random_element(algorithm='default')

Returns a random element of self, optionally using the algorithm argument to decide how it generates the element. Algorithms currently implemented:

• default: Choose an integer $$k$$ using the standard distribution on the integers. Then choose an integer $$a$$ uniformly in the range $$0 \le a < p^N$$ where $$N$$ is the precision cap of self. Return self(p^k * a, absprec = k + self.precision_cap()).

EXAMPLES:

sage: Qp(17,6).random_element()
15*17^-8 + 10*17^-7 + 3*17^-6 + 2*17^-5 + 11*17^-4 + 6*17^-3 + O(17^-2)

An implementation of the $$p$$-adic integers with capped absolute precision.

An implementation of the $$p$$-adic integers with capped relative precision.

An implementation of the $$p$$-adic integers using fixed modulus.

fraction_field(print_mode=None)

Would normally return $$\mathbb{Q}_p$$, but there is no implementation of $$\mathbb{Q}_p$$ matching this ring so this raises an error

If you want to be able to divide with elements of a fixed modulus $$p$$-adic ring, you must cast explicitly.

EXAMPLES:

sage: ZpFM(5).fraction_field()
Traceback (most recent call last):
...
TypeError: This implementation of the p-adic ring does not support fields of fractions.

sage: a = ZpFM(5)(4); b = ZpFM(5)(5)

#### Previous topic

Unramified Extension Generic


text:
qrmtools v0.0-12

0

0th

Percentile

Tools for Quantitative Risk Management

Functions and data sets for reproducing selected results from the book "Quantitative Risk Management: Concepts, Techniques and Tools". Furthermore, new developments and auxiliary functions for Quantitative Risk Management practice.

Functions in qrmtools

 Name Description NA_plot Graphical Tool for Visualizing NAs in a Data Set Black_Scholes Black--Scholes formula and the Greeks GPD_shape_plot Fitted GPD Shape as a Function of the Threshold GEV Generalized Extreme Value Distribution GEV_shape_plot Fitted GEV Shape as a Function of the Threshold ARMA_GARCH Fitting ARMA-GARCH Processes GPD (Generalized) Pareto Distribution VaR_ES_bounds Worst and Best Value-at-Risk and Best Expected Shortfall for Given Marginals GPDtail GPD-Based Tail Distribution (POT method) alloc Computing allocations fit_GPD Parameter Estimators of the Generalized Pareto Distribution fit_GEV Parameter Estimators of the Generalized Extreme Value Distribution fit_GARCH_11 Fast(er) and Numerically More Robust Fitting of GARCH(1,1) Processes catch Catching Results, Warnings and Errors Simultaneously pp_qq_plot P-P and Q-Q Plots returns Computing Returns and Inverse Transformation edf_plot Plot of an Empirical Distribution Function tests Formal Tests of Multivariate Normality get_data Tools for Getting and Working with Data risk_measures Risk Measures matrix_plot Graphical Tool for Visualizing Matrices tail_plot Plot of an Empirical Surival Function with Smith Estimator hierarchical_matrix Construction of Hierarchical Matrices matrix_density_plota Density Plot of the Values from a Lower Triangular Matrix mean_excess Mean Excess No Results!


text:
Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/412

 Title: Asymptotic Behaviour of Colength of Varieties of Lie Algebras Authors: Mishchenko, S.Zaicev, M. Keywords: Lie Algebras With Polynomial IdentitiesVarieties Of Lie AlgebrasCodimensionsColength Issue Date: 2000 Publisher: Institute of Mathematics and Informatics Citation: Serdica Mathematical Journal, Vol. 26, No 2, (2000), 145p-154p Abstract: We study the asymptotic behaviour of numerical characteristics of polynomial identities of Lie algebras over a field of characteristic 0. In particular we investigate the colength for the cocharacters of polynilpotent varieties of Lie algebras. We prove that there exist polynilpotent Lie varieties with exponential and overexponential colength growth. We give the exact asymptotics for the colength of a product of two nilpotent varieties. Description: This project was partially supported by RFBR, grants 99-01-00233, 98-01-01020 and 00-15-96128. URI: http://hdl.handle.net/10525/412 ISSN: 1310-6600 Appears in Collections: Volume 26 Number 2

Files in This Item:

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text:
# [java] Eclipse, SWT, Jar files

This topic is 5066 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

I recently wrote a small application for my brother, I used the Eclipse IDE and for the GUI i used SWT. I have several problems i just can't really fix. 1. I cannot get a exec jar file to work (i am thrown errors)...Most likely I am not setting it up right, within eclipse itself the app works perfectly. I was wondering how I can make an exec jar file for my brother to run. 2. I am pretty sure that even if i get the exec jar file to run on my system..due to him not having eclipse installed (ie. no swt library) he will not be able to run this application. How would I go about handling this? Thx for any help. ippo. ps. If you don't feel like explaining this but do know of a good resource to read..feel free to just post a link. In my searches I am coming up with nothing (or perhaps i just don't know what i'm looking for)

##### Share on other sites
Hi,

There are several things to consider when using a JAR file.

1. Dependencies. When you have simple .class files, you can have dependencies, like SWT, in another JAR file, as long as you have that filein your CLASSPATH. I *think* you can't have the JAR file in your main JAR file - it wouldn't work - at least I haven't been able to get it to work. So, you would have to extract all dependencies and compress them as simple .class file with your own app into the JAR. So, in your case, you'd have to get all the SWT files out of their own JAR, and into yours - being careful to preserve the package structure, of course.

2. Program resources. If you are using stuff like images, or text files, and such in your program, then you have to load them through the Class.getResource method (or one of it's siblings, like System.getSystemResource, I think). The java.io.File will *not* work inside a JAR.

3. ... Ehhh, there was something else I was gonna say... :)

Ohhh, yeah.

3. Manifest file. You gotta tell the JAR file which class you want to run. So, inside you have to have the file META-INF/MANIFEST.MF, inside which you have to have a line which reads something like this:

Main-Class: fully.qualified.ClassName

[smile]

Hope that helps.

Vovan

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bleh, i still can't get it...

i get the "Illegal thread exception" error..which probably has to do with the usage of swt... I pointed the classpath to swt, but no luck. Oh well..

thx for the help tho ;)

ippo.

/me breaks out the c++

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Hi,

Pfft, don't give up so easy there. [smile] Figured stuff like this out is where the fun's at. ;)

Also, I never heard of an illegal thread exception... (Granted, I never used SWT...) If you post the actual name of the exception it spits out and the message, maybe that would help us help you. [grin]

Vovan

##### Share on other sites

Sorry, it was "fatal" not "illegal". It is most likely because SWT is not setup to run right. Also, if i run it from the command line..it tells me the main class isn't found..which i think is bs because my manifest file points right to it :/ I guess now that I already ported what i was doing to c++ and sent it off will give me more time to fix this problem so it won't happen in the future..

[Edited by - ippo on August 5, 2004 1:24:44 PM]

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Quote:
 Original post by ippo Sorry, it was "fatal" not "illegal". It is most likely because SWT is not setup to run right. Also, if i run it from the command line..it tells me the main class isn't found..which i think is bs because my manifest file points right to it :/ I guess now that I already ported what i was doing to c++ and sent it off will give me more time to fix this problem so it won't happen in the future..
yeah, you don't have the manifest setup properly, it's nothing wrong with your code.

##### Share on other sites
^

that's exactly what i have been doing...

the only thing differnce i have is the main class is part of a package so it comes out being like "launcher.Launcher" for the Main class, that really shouldn't be a problem though..should it?

##### Share on other sites
No it shouldn't. Can you post your manifest file so that we can have alook at it and determine if there is anything wrong with it.

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Hi,

And also make sure that the manifest file is in the correct directory inside the JAR. [smile]

+ app.jar  |  +- META-INF  | |  | +- MANIFEST.MF  |  +- launcher  | |  | +- Launcher.class  | +- AnotherLauncher.class  |  +- otherpackage  +- ...

[smile]

Vovan

EDIT: Oh, I guess you are generating the JAR automatically... So it should be put where it belongs...

##### Share on other sites
Manifest-Version: 1.0Sealed: trueMain-Class: gui.Launcher

is the contents of my file...

and ^, that is how my project looks..almost exactly ;d (gg test/example name usage ;d)

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### THE EFFECTS OF THREE SERVICE DELIVERY MODELS ON VOCABULARY LEARNING BY SECOND-GRADE CHILDREN

Laura Glastetter-Stone
Speech-Language Pathologists (SLPs) provide services to children in schools across the United States primarily in a direct small group service delivery model outside of the regular education classroom. To date little research exists to indicate that direct pull-out service delivery is an effective model in elementary schools for students requiring speech and language therapy. One area that has been studied is the effectiveness of vocabulary intervention among service delivery models. Preliminary findings suggest that students...

### A BIOPHYSICAL INVESTIGATION OF STABILITY, LIGAND BINDING, AND IRON STATE OF CYP102A1

Catherine Denning
Cytochrome P450s (CYPs) are cysteine ligated Fe-heme monooxygenases that are found in all domains of life. In mammals, they have a role in xenobiotic metabolism and steroid synthesis, making them a fundamental requirement for survival. In addition, their ability to perform a variety of chemical reactions on an array of substrates makes CYPs highly sought for biotechnical applications such as wastewater remediation, production of potential drug candidates, and creation of drug metabolites. By mutating specific...

### Fiscal Year 2011 FHWA-536 Report for the Kentucky Transportation Cabinet

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The Federal Highway Administration (FHWA) requires state transportation agencies to submit a biennial report on local highway finances. The purpose of these reports is to provide FHWA with the data it needs to capture the financing of highway activities at the local level. Based on this information, it can identify trends in revenue, expenditures, investments, and program development, and in turn make decisions about future investments. The report, FHWA-536, asks agencies to report on four...

### A MULTI-METHOD INVESTIGATION OF THE MODERN SEDIMENTATION AND LATE HOLOCENE PALEOLIMNOLOGY OF JUNE LAKE (MONO COUNTY, CA), AND A SURVEY-BASED ANALYSIS OF NINTH GRADERS’ ATTITUDES TOWARDS GEOLOGY

Eva Lyon
Three distinct manuscripts comprise this dissertation. The first analyzes the modern sedimentary basin of June Lake, a small glacial lake in the eastern Sierra Nevada of California (USA) using a number of data sets, including bathymetry, surface sediment composition, and seismic stratigraphy. The seismic survey revealed sublacustrine morphological features that suggest the basin originated due to ice scour, as well as four acoustically distinct stratigraphic units that reflect the history of sedimentation following glacial scouring....

### TOBACCO USE AND NICOTINE WITHDRAWAL AMONG PATIENTS WITH MENTAL ILLNESS

Yazan Al-Mrayat
People with mental illness (MI) are disproportionately affected by tobacco use compared to the general population. In fact, it is estimated that people with MI consume approximately 44% of cigarettes smoked in the United States. Moreover, the MI population is at greater risk for the negative social, economic, and health consequences associated with tobacco use and are reported to have 25-year shorter life expectancies than the general population. The impact of tobacco use is further...

### HIGH FREQUENCY OSCILLATIONS IN THE EPILEPTIC BRAIN

AMIR AL-BAKRI
About a third of all epilepsy patients may experience seizures that are resistant to medication. Surgical resection may be an option for some of these patients, but localization of the epileptogenic zone is difficult and expensive. For this process, the seizures must be observed and recorded in a clinical setting over several days. High-frequency oscillations (HFOs) have emerged as a possible biomarker for predicting the epileptogenic zone from a brief interictal recording of brain electrical...

### THE INFLUENCE OF CRYOGENIC MACHINING ON SURFACE INTEGRITY AND FUNCTIONAL PERFORMANCE OF TITANIUM ALLOYS FOR BIOMEDICAL AND AEROSPACE APPLICATIONS

Ying Sun
The excellent properties of titanium alloys such as high strength, as well as good corrosion and fatigue resistance are desirable for the biomedical and aerospace industry. However, the same properties that make titanium alloys desirable in high-performance applications also make these space-age materials “difficult-to-machine” materials, as the titanium alloys exhibit high cutting temperatures because of their high strength and low thermal conductivity. Cryogenic machining is a severe plastic deformation (SPD) processes which uses liquid nitrogen...

### INVESTIGATION INTO MINE PILLAR DESIGN AND GLOBAL STABILITY USING THE GROUND REACTION CURVE CONCEPT

Ravi Chandan Ray
Pillars form an important support structure in any underground mine. A bulk of the overburden load is borne by the mine pillars. Thus, the strength of pillars has been a subject of detailed research over more than 6 decades. This work has led to the development of largely empirical pillar design formulations that have reduced the risk of pillar failures and mine collapse. Current research, however, has drawn attention to the fact that some of...

### RESIDENTIAL RADON EXPOSURE, ITS CONTRIBUTION TO LUNG CANCER, AND SOCIAL DETERMINANTS OF RADON TESTING

Stacy Stanifer
Lung cancer is a highly preventable form of cancer. Cigarette smoking is the leading cause of lung cancer followed by radon gas exposure and exposure to secondhand smoke. Kentucky leads the nation in both incidence and mortality from lung cancer. Tobacco use in Kentucky continues to be a major public health concern as nearly one-quarter of adults report current tobacco use and just over one-third of Kentucky homes with children lack rules which prohibit smoking...

### POPULATION PHARMACOKINETIC MODELING AND GENETIC ASSOCIATION ANALYSIS IN INFANTS WITH NEONATAL ABSTINENCE SYNDROME RECEIVING MORPHINE OR CLONIDINE

Fei Tang
Neonatal abstinence syndrome, or NAS, is a postnatal opioid withdrawal syndrome occurring in 55% to 94% of neonates as a result of in utero exposure to opioids. It has emerged as a significant public health issue, as its incidence more than quadrupled in the past decade. There is significant variability in disease severity and treatment outcomes in neonates with NAS due to patient-specific factors and treatment- or site-specific factors. To understand what contributes to variability...

### LASER ABLATION IN LIQUID FOR THE CONTROLLED PRODUCTION OF PHOTOLUMINESCENT GRAPHENE QUANTUM DOTS AND UPCONVERTING NANOPARTICLES

Rosemary Calabro
Photoluminescent (PL) nanomaterials play an important role in areas including displays, sensing, solar, photocatalysis, and bio applications. Traditional methods to prepare PL materials suffer many drawbacks such as harsh chemical precursors, complicated synthetic steps, and production of many byproducts. Laser ablation in liquid (LAL) has emerged as a promising alternative to prepare materials that is single-step, fast, uses fewer precursors, produces fewer side products, and has simple purification steps. During LAL, a solid target is...

### COARSE-GRAINED DYNAMICALLY ACCURATE SIMULATIONS OF IONIC LIQUIDS AT VACUUM-INTERFACE

Tyler Stoffel
Ionic liquids, possessing improved properties in many areas of technical application, are excellent candidates as components in development of next-generation technology, including ultra-high energy batteries. If they are thus applied, however, extensive interfacial analysis of any selected ionic configuration will likely be required. Molecular dynamics (MD) provides an advantageous route by which this may be accomplished, but can fall short in observing some phenomena only present at larger time/length scales than it can simulate. Often...

• 2020
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• Text
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• Dataset
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#### Affiliations

• University of Kentucky
597
• University of California, San Diego
4
• National Institutes of Health
3


text:
MathSciNet bibliographic data MR207204 (34 #7020) 65.55 Couot, Jacques Application des suites $m\theta$$m\theta$ á l'intégration numérique. (French) C. R. Acad. Sci. Paris Sér. A-B 264 1967 A183–A186. Links to the journal or article are not yet available

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