Fractional/Final Time: 22.160, 46.050, 58.840, 00.000, 00.000, 1:05.710.
Fractional/Final Time: 22.010, 45.970, 58.890, 00.000, 00.000, 1:05.790.
Fractional/Final Time: 24.290, 49.860, 1:15.240, 1:42.540, 00.000, 1:44.990.
Fractional/Final Time: 23.640, 48.200, 1:13.560, 1:39.290, 00.000, 1:45.530.
Fractional/Final Time: 23.080, 45.880, 1:11.070, 00.000, 00.000, 1:24.080.
Fractional/Final Time: 24.430, 49.040, 1:12.650, 1:24.890, 00.000, 1:37.440.
Fractional/Final Time: 22.220, 45.740, 58.520, 00.000, 00.000, 1:11.880.
Fractional/Final Time: 23.950, 49.140, 1:13.300, 1:25.250, 00.000, 1:36.920.
Scratched: Northern Wind, Lady Love.
Fractional/Final Time: 22.900, 47.000, 1:11.150, 1:23.620, 00.000, 1:36.120.
$0.5 Pick 3 (1-9-1) 3 Correct Paid $24.80. $1 Daily Double (9-1) paid $18.30; $1 Exacta (1-4) paid $13.70; $0.1 Superfecta (1-4-2-5) paid $11.49; $0.5 Trifecta (1-4-2) paid $17.05; $1 X-5 Super High Five (1-4-2-5-3) paid $375.20; Attendance 2,547. $. $.
Fractional/Final Time: 24.870, 48.210, 1:13.550, 00.000, 00.000, 1:26.360.
$0.5 Pick 5 (6-1-9-1/7-10) 5 Correct Paid $6,771.90. $0.5 Pick 4 (1-9-1/7-10) 4 Correct Paid $142.10. $0.5 Pick 3 (9-1-10) 3 Correct Paid $56.10. $1 Super High Five (10-7-3-1-5) no winners.; $0.5 Trifecta (10-7-3) paid $88.70; $1 Daily Double (1-10) paid $22.40; $1 Exacta (10-7) paid $32.80; $0.1 Superfecta (10-7-3-1) paid $124.36; Attendance 2,547. $179,863. $3,271,804. Handle $163,056. Total Handle $3,614,723.


It was a tight race that threatened to end Kenya's dominance in the regional cross country, but only just.
"I am very happy to get this opportunity to represent my country. My guard has been up, I am ready for the challenge," says Muzamir Kakande.
The 12-strong team will not take part in Italy due to financial constraints.
"The players who are taken to camp will be trained for the Under 19 qualifiers that start next year."
The top qualifiers overall shall then participate in the finals.
Proscovia's low tally saw her drop two places to third position on the scorers' chart with 226 goals in 267 attempts.


Macanudo Prince Phillip Maduro brings you warm and welcoming maduro character in a 7 1/2 x 49 Churchill vitola.
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Macanudo and Maduro are two words that go together like Jenny's peas and carrots. What dark secrets only Macanudo knows about how to get the best out of Connecticut Broadleaf Maduro wrappers is a mystery; but the results are magical. As it burns the caramelization of the maduro wrapper's abundant sugars and oils creates a sweet aroma. This is a very smooth and mild to medium cigar. Creamy mocha flavors hold consistent throughout accompanied by hints of cedar, honey, and mushrooms with a long pleasant finish. As a testament to Macanudo's usual high construction qualities, the burn was perfectly even to the end and the white ash held on for more than an inch before each drop.
Of all the maduro's I have smoked, the Prince Phillip is the smoothest, easy draw and a pleasing taste. A nice balanced size and priced right.
Macanudo Prince Phillip Maduro is rated 4.9 out of 5 based on 3 customer ratings.


A unique Latin inspired blend of 14 different herbs and spices.
Our Acapulco Gold Blend is a unique blend of 14 different Latin inspired herbs and spices including fresh oregano, chili powder, cumin and cayenne. Amazing on ribs and makes the best fajitas ever!


Becky Beaupre Gillespie once said, "Good enough is the new perfect." Stop chasing perfection. Perfection suggests a state of flawlessness, without any defects. To be perfect implies a condition where your action or performance attains a level of excellence that cannot be exceeded.
Throughout my career I've worked with people that I've never met in person. In theory, I could spend an entire day without meeting another human face-to-face. But could this kind of self-imposed isolation become standard working practice in the future?
Over the last year, my role at Buffer has changed from an individual contributor to a technical leadership role.While the amount of time I spend coding and doing architecture hasn't changed much, the way I go about the tasks has changed significantly.
A book I'm reading: Stealing Fire: How Silicon Valley, the Navy SEALs, and Maverick Scientists Are Revolutionizing the Way We Live and Work by Steven Kotler and Jamie Wheal. It's a guidebook for anyone who wants to radically upgrade their life.


text:
Here's how your mental health depends on collective wellbeing
Our wellbeing depends on the groups we are part of.
Image: Photo by Antor Paul on Unsplash
Geoff Mulgan Professor of Collective Intelligence, Public Policy and Social Innovation, University College London (UCL)
How the Forum's networks have navigated the global response to COVID-19
Mental health is nearly always seen as an individual issue requiring individual solutions. Yet in reality it's as much a problem for groups and organizations.
One legacy of the COVID-19 crisis could be a revolution in how we measure mental health and promote recognition that our wellbeing depends very much on the groups we are part of.
This would also promote positives – and help us understand what makes groups thrive.
The COVID-19 crisis has seriously damaged mental health all over the world. A high price has been paid by many children who've missed out on time with friends and school, and many of the elderly have felt isolated. The challenges and solutions are well documented by the International Public Policy Observatory on COVID.
But the crisis is also shining a light on the stresses faced by employees. In the UK, new evidence on health workers shows that nearly half of those working in intensive care units suffered from severe anxiety, depression, post-traumatic stress disorder, or harmful use of alcohol. There may be similar patterns in other groups on the front-line, but we just don't know. And this is highlighting a bigger problem in how we look at mental health. It is nearly always seen as an individual issue requiring individual solutions. Yet in reality it's as much a problem for groups and organizations.
In everyday conversation we often talk of toxic cultures and of dysfunctional organizations. We know that individuals who join such organizations are powerfully affected by them: collective mental health influences individual mental health. There can be a pervasive culture where employees are depressed, deluded or prone to compulsive behaviours.
We need to talk about mental health at work, say employees
The priority for workplaces in the new normal? Wellbeing
The best starting point for addressing problems is usually to find ways to see or map them. Unfortunately, we lack rigorous definitions of what these collective mental states might be. We lack good and comparable measures, despite an explosion of psychometrics and surveys.
Psychiatry has a powerful tool to help solve this at the individual level. The DSM is the 'Diagnostic and Statistical Manual of Mental Disorders' that is the bedrock of American psychiatry. It is revised periodically – the most recent version is DSM5 - and is meant to capture the latest state of knowledge.
There is much that can be challenged in it. It rests on a pretty weak evidence base (only a tiny percentage of psychology experiments are successfully replicated); it uses often arbitrary categories; it lacks much solid knowledge about causal mechanisms; and it's prone to ideological bias (homosexuality was only taken out of the DSM in the early 1970s – before that it was treated as a disease).
But it does at least provide some coherence. For groups and companies we could do better. Recent years have brought rapid growth in survey data on anxiety levels, depression and optimism. Through social media, a treasure trove of data on moods, beliefs and anger is now available. The data is rarely straightforward – and there will always be a gap between what people say and what they feel. But this sea of data provides a good starting point, and possibilities that couldn't have been imagined a decade or two ago, some of them quite scary, from analysis of company emails to analysis of facial expressions during Teams meetings.
People are reporting the pandemic has negatively impacted their emotional and mental health.
Image: Ipsos-World Economic Forum
So what might the categories be for new maps of collective mental health? An obvious one is depression. The usual definitions of depression include being unhappy or hopeless, having low self-esteem and finding no pleasure in things you usually enjoy. Our interest should be in spotting this in groups or whole populations where, although there is a wide range of levels of depression, the normal distribution curve has been shifted.
Delusion also looks relevant. The Cleveland Clinic defines delusional disorder as 'a type of serious mental illness in which a person cannot tell what is real from what is imagined', associated with 'an irritable, angry, or low mood, and hallucinations (seeing, hearing, or feeling things that are not really there)'. Again, this is quite common in groups and even nations.
A third example is obsessive compulsive behaviour which is when an unwanted, intrusive and often distressing thought, image or urge repeatedly enters people's minds, causes them distress and is associated with repetitive behaviours. This certainly looks recognizable at a group or collective level.
Fourthly, PTSD is clearly relevant – particularly for groups like the military or medical staff, and emergency services, that often have to face traumatic situations. The US army, for example, introduced extensive programmes to deal with PTSD a decade ago, led by Brigadier General Rhonda Cornum, using the language of psychological fitness and resilience. Again, however, the emphasis was very much on individual diagnosis and treatment.
Each of these conditions – depression, delusion, compulsive behaviour and trauma - could be diagnosed at an aggregate or average level. But we would expect there to be big differences within groups and organizations. Status and power correlate fairly well with measures of physical and mental health. So any new methods of measurement need to look at the differences as well as the averages.
The importance of such differences was highlighted in recent research by Angus Deaton and Ann Case on 'diseases of despair' which showed the serious decline in both mental and physical health amongst predominantly middle-aged men in the US whose status had declined.
What is the World Economic Forum doing to champion social innovation?
Social innovators are addressing the world's most serious and entrenched challenges, ranging from illiteracy to clean water and sanitation, girls' education, prison reform, financial inclusion and disaster relief.
The Schwab Foundation for Social Entrepreneurship is supporting more than 400 leading social innovators operating in over 190 countries.
Since its foundation in 1998, a total of 722 million lives have been directly improved by the work of this community of leading social innovators.
Our global network of experts, partner institutions and World Economic Forum constituents are invited to nominate outstanding social innovators.
Visit the Schwab Foundation website for more information about the award process and the selection criteria.
Read more about the Foundation's impact.
Many organizations use wellbeing indicators – covering levels of anxiety, satisfaction with job, pulse surveys and Net Promoter Scores as a measure of engagement. Two widely validated questions, which could be used as standard parts of future measures, are: "In the past 3 months, have you ever not felt well enough to perform your duties to your normal standard, but attended work regardless?" and 'do you feel energized by your work'.
If we had better measures we could use them not just to address negative patterns but also to promote positives – to understand what helps groups to thrive. This has been the message of the 'positive psychology' movement and many nations now measure happiness, offering important insights. The best predictors in the annual World Happiness Report are survey answers to the question of whether you had friends or relatives you could rely on in a crisis. We might expect that to matter for firms and groups too. An organization I helped found – Action for Happiness – for example, now has very powerful evidence on how to boost both wellbeing and feelings of social connectedness.
One legacy of the COVID-19 crisis could be a revolution in how we measure mental health and recognition that our own mental health depends very much on the groups we are part of. Anecdotes about toxic employers and deluded nations could be more grounded in data. With new measures we could start to harness that data to improve not just our individual mental health but our collective mental health too.
This article is part of a Wellbeing Series, launched by the Forum and the Schwab Foundation, with the idea to support the human aspects of social entrepreneurship to unleash the potential for social change.
Geoff Mulgan, Professor of Collective Intelligence, Public Policy and Social Innovation, University College London (UCL)
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Report — 24 November 2021

redpajama_set_name: RedPajamaCommonCrawl


More streamlined interface – The interface has been stripped down to bare minimum with navigation streamlined to maximum extent. I got a lot of feedback (100+ mails) regarding the look of website & implemented the most sought out changes here.
Faster loading time – Now thats a real gem. the loading time has been decreased by more than 55% to 4.38 seconds as compared to staggering 11 seconds earlier. See the stats for Prohack & Mobile version courtesy of GTmetrix , click here to see the actual stats in realtime . Also, better Yslow & Pagespeed scores have been attained, as compare to older version which scored way below in both these parameters.
Advertising rates shed down – The name says it all, go to advertising section for more details.
Brand new propaganda – Its what I leave upto You to decide. However I will be having a tactical shift to more tech oriented articles with practical guides.
Plus, small changes have been implemented at the website, which you will experience in your stay.
thanks for launching the mobile version !!


If you were to look at your typical day, how many tasks are aided by convenience? With the advent of smartphones, the rapid growth of the Internet and mobile connectivity we are constantly finding more convenient ways to get many things done without too much hassle. We have easy access to all sorts of information, news, and have the ability to shop online any time of the day or night from the comfort of your own home. We now value convenience. We have become spoiled by immediacy and are annoyed by tasks that remain at the old level of effort and time. Not surprisingly, as task after task becomes easier, the growing expectation of convenience exerts a pressure on everything else to be easy or get left behind. Convenience has emerged as perhaps the most powerful force shaping our individual lives and our economies.
But it wasn't always like this. Convenience as we now know it is a product of the late 19th and early 20th centuries, when labor-saving devices for the home were invented and marketed. Milestones include the invention of the first "convenience foods," such as canned pork and beans and Quaker Quick Oats; the first electric clothes-washing machines; cleaning products like Old Dutch scouring powder; and other marvels including the electric vacuum cleaner, instant cake mix and the microwave oven. Then in the 1960's came the Automated Teller Machine (ATM), the first conception of self-service technology (SSS). Since then, due to the advancements in technology, self-service technologies have come a long way and are now almost everywhere in every industry in various forms such as mobile banking, online shopping, e-support, virtual agents, self-serve luggage stations, on-demand concierge apps, hotel delivery bots, online tracking, kiosks from photo-printing, to airport and hotel check-in, grocery shopping, digital food ordering – the list is endless.
Automation, smart technologies and self-service achieve various new advances every day fuelling and feeding our appetite for convenience. "After you have experienced streaming television, waiting to see a show at a prescribed hour seems silly, even a little undignified. To resist convenience — not to own a cellphone, not to use Google — has come to require a special kind of dedication that is often taken for eccentricity, if not fanaticism." Tim Wu, Law Professor at Columbia. With our constant desire for convenience, customers increasingly expect self-service technology options and now expect to be able to have more visibility and control when it comes to interacting with a business. More than 85% of consumers have used a self-service options when they shop, with 73% of consumers saying they prefer self-service technologies, such as self-checkout, over engaging with brand associates. At the same time, about 76% of respondents said brands that use mobile technology—in the form of both self-service mobile tools and mobile tools used by employees helps provide a more efficient experience.
With customers preferring to use machines to get their services instead of interacting with an assisted service worker self-service is growing exponentially in all areas of retail, travel and hospitality, restaurants, healthcare and banking environments. It is estimated that by 2023 the global self-service technology market will generate a market value of USD 32 billion, growing at a CAGR (compound annual growth rate) of 13%.
Basically, the simple fact is; people enjoy using self-service options because the technology makes life more efficient. As the demand for self-service technologies continues to rise businesses will need to provide their clients with the resources that empower them with the ability to create services that are independent of immediate staff participation or risk being left behind.
When asked what guest-facing technologies hotels will focus on in the coming year, two out of three hoteliers asked by HotelNewsNow said voice-enabled technology. The third focused on automation via mobile apps. And these may well be where these particular properties need to focus with their ideal guests. While some technology trends are elements that hotels need to survive, others are simply a fad. So how can a hotelier strategically decipher which technology they should invest in?
Get to know your guests: Succeeding in the hospitality industry means succeeding in the delivery of exceptional guest service — so when it comes to technology, the guest should always be front and center. The concept of putting the customer first is not new, but knowing how to stay relevant requires staying up to date with their evolving needs. Generally speaking, older technology solutions are not able to provide the guest insights that will empower the level of personalized, attentive service required to meet your guest's evolving service expectations. Rather, hoteliers should look to progressive technology solutions that offer real-time, visual data analytics with actionable insights at every touch point of each guest's stay.
Future Proof Your Investments: Regardless of what technology solutions you are thinking of investing in, one thing that every hotel needs to start with is a solid PMS backbone. With a core PMS, one that is cloud-based with open APIs can change the way hoteliers do business. Compared to traditional solutions, with a cloud-based PMS, hoteliers stand to gain from having a flexible IT infrastructure. Its' true power lies in how seamlessly it can integrate with other systems; allowing hotels become more nimble, to connect and do business more seamlessly and can scale up or scale down operations enabling to support business growth without expensive changes to your existing systems. With a solid cloud-based PMS foundation in place, from there, you have the flexibility to integrate and build exactly what will make your guests happy, and make your property more profitable into the future.
Be Mobile, or Be Left Behind: Similar to the PMS, mobile is something that cannot be avoided in the hotel industry. It is no longer an emerging trend — it's long since invaded hospitality territory. Mobile devices have become part and parcel of our everyday and is changing the way people perceive what constitutes good service. Consumers are coming to expect the kind of self-service, streamlined experience that mobile technology provides. They want the freedom to choose how and when they interact with your hotel, they want the ability to help themselves, to be self-sufficient. By offering guests self-service options satisfies an expanded definition of customer service now grounded by the conveniences of the instant gratification economy.
Try Before You Buy: This heading is a little self-explanatory! However, as mentioned earlier, there is a vast amount of hotel technology saturating the market. There are a lot of different providers providing a range of tools and solutions and it can be hard to decipher which solution best aligns with your business needs. Many companies do offer trials and it is wise that you test any new solution before making any final commitment to ensure that it isn't something that doesn't perform as advertised or is unnecessary.
While there nearly seems to be a new technological solution, innovation or trend every other day that hoteliers are expected to keep up-to-date with the reality is every hotel has different needs, different guests, and different concepts. Before investing in any new technology solution, hotels need to think carefully about the problems that need solving and what they're hoping to achieve with the technology they plan to invest in. A key takeaway would be to focus on a building a foundation that will offer flexibility and empowers you to make your guests happy, and your property more profitable.
Today's travelers start their journeys online. Trips that used to require travel agents can now be planned entirely from a mobile phone. A Google search is often the first step an aspiring traveler takes when researching their trip, so it's essential for your hotel to be discoverable online. Search Engine Optimization, or SEO, can be used to boost your Google rankings, and ensure that travelers find you when searching in your area.
Does your hotel cater to business travelers, or are you a boutique establishment procuring unique experiences for your guests? No matter who your target audience is, it's essential to know them well. Research the latest trends that your target market is interested in and offer an experience that is uniquely catered to their travel needs and desires. Unless you're promoting a rustic, throwback hotel experience, embracing technology trends such as mobile check-in and self-service kiosks are effective ways to target the modern, mobile traveler.
Your marketing efforts should not be flat all year round. They need to ebb and flow with the travel seasons in order to target the swells of potential guests coming through your location. Keep in mind that they're likely booking their journeys well ahead of time, so your marketing budget should be expanded for some time before the peak season starts.
In order to stay competitive, your hotel needs to stand out. Incentives such as time-sensitive discounts allow you to make a mark on potential guests, even if you're not dominating the local market. You can even offer rewards systems that give special rates or complementary benefits to your most loyal customers. Make your deals irresistible with customer incentives, and your bookings are sure to see a boost.
Local business in your area are always on the lookout for mutually beneficial partnerships. Local promotions can be a great way to make a mark on your city or town, and get people talking about your business. This can also include local contests and promotions that build hype and get people talking about your hotel brand.
Nowadays, picking up the room phone and calling the front desk feels like an antiquated activity for many guests. Instead, open up the communication channels that customers have with your staff by using mobile chat and click-to-call features. Modern hotel property management systems such as StayNTouch integrate this connectivity directly into their platforms to make staying connected with guests easier than ever.
Good hospitality is par for the course when it comes to the hotel industry. Consider what your business can do to be exceptional. Going above and beyond with your customer service will help you to earn positive online reviews and stand out from the competition. If you have a guest that has an issue with their stay, do everything you can to resolve it. Your entire staff should feel that customers come first and reflect this in their level of service. Inspire them to go above and beyond and see the results!
Your social media presence serves as a key part of your brand identity. Staying active on social media means not only posting content regularly but also interacting with fellow users. Remember that responding to comments and sharing content from other pages is a public display of your hotel's values and vision. Take care to curate content and replies that follow the best interests of your brand.
Believe it or not, a great website experience can translate into a great hotel experience in the minds of your visitors. A website that is outdated shows that your business may not care about the details that differentiate an average hotel from an outstanding one. Make sure your webpages are responsive and intuitive to use and have all of the information site visitors may need about your hotel. It's a good idea to include a "Frequently Asked Questions" section to cover the common inquiries surrounding your hotel.


text:
\section{Introduction}

Data interpolation and statistical regression of noisy data are both classical subjects but their domain of application have been disjoint until recently. Scattered data interpolation techniques \cite{wendland2004scattered} are generally used for clean data. On the other hand, when supervised learning or statistical regression techniques are applied to noisy data, in general smoothing or regularization methods are applied to prevent training data interpolation, as the latter is believed to lead to poor generalization \cite{james2013introduction}. However, accumulating empirical evidence from overparameterized deep networks has shown that data interpolation (equivalently, zero error on the training set) does not automatically imply poor generalization \cite{zhang2017understanding,belkin2018understand}. This has in turn given rise to a rapidly growing body of theoretical work to understand how and why noisy data interpolation can still lead to good generalization \cite{cutler2001pert,wyner2017explaining,belkin2018overfitting,rakhlin2018consistency,ongie2019function,belkin2019reconciling,liang2018just,bartlett2019benign,montanari2019generalization,karzand2019active,xing2018statistical}.

A key observations in this regard is the phenomenon of Statistically Consistent Interpolation \cite{mitra_fitting_2021}, {i.e.}, regression function estimation that interpolates training data but also generalizes as well as possible by achieving the Bayes limit for expected generalization error (risk) when the sample size becomes large. This hints at a rich set of theoretical questions at the interface between the disciplines of scattered data interpolation and supervised learning, that have only begun to be addressed. In particular, there has been comparatively little study of the generalization error or risk of interpolating learners. Computation of generalization error bounds in machine learning often relies on the capacity of the class of fitting functions \cite{ab-nnltf-99}, however such model complexity based bounds are not tight enough to be useful for interpolating learners \cite{belkin2018understand}. For nonparametric interpolation approaches such as that considered here, it is also not clear what model complexity means. Thus, there is a need for other approaches to understanding the generalization behavior of nonparametric interpolating learners, including more direct treatments of the generalization error for specific interpolation schemes so as to gain better theoretical understanding. The current paper addresses this need.

We present a detailed analysis of the finite-sample risk of an interpolating learner with intriguing theoretical properties, the Hilbert kernel estimator (Devroye {\it et. al.} \cite{devroye1998hilbert}). A unique property of this Nadaraya-Watson (NW) style estimator \cite{nadaraya1964estimating,watson1964smooth} is that it is fully parameter-free and does not have any bandwidth or scale parameter. It is global and uses all data points for each estimate: the associated kernel is a power law and thus scale-free. Although statistical consistency of this estimator was proven \cite{devroye1998hilbert} when it was proposed, there has been no systematic analysis of the associated convergence rates and asymptotic finite sample behavior. We provide this analysis in the present study.

{\bf Related work} The only other interpolation scheme we are aware of, that is proven to be statistically consistent in arbitrary dimensions under general conditions, is the recently proposed weighted interpolating nearest neighbors method (wiNN) \cite{belkin2018overfitting}, which is also a NW estimator utilizing a singular power law kernel of a very similar form but with two important differences: a finite number of neighbors $k$ is utilized (rather than all data points), and the power law exponent $\delta$ of the NW kernel satisfies $0<\delta<d/2$ rather than $\delta=d$. To achieve consistency $k$ has to scale appropriately with sample size. Despite the superficial resemblance, the wiNN and Hilbert Kernel estimators have quite different convergence rates, as we will see from the results of this paper. Also worth mentioning is the Shepard interpolation scheme \cite{shepard1968two} originally proposed for interpolation of 2D geospatial data sets, also a NW style interpolating estimator, though used in the context of scattered data interpolation. In scattered data interpolation \cite{wendland2004scattered}, the focus is generally on the approximation error (corresponding to the ``bias'' term in our analysis below). The approximation error of the Shepard scheme has been analyzed \cite{farwig1986rate} but as we will see below the risk for Hilbert kernel interpolation is dominated by the noise or ``variance'' term. In contrast with wiNN or Hilbert kernel interpolation, other interpolating learning methods such as simplex interpolation \cite{belkin2018overfitting} or ridgeless kernel regression \cite{liang2018just} are generally not statistically consistent in fixed finite dimension \cite{rakhlin2018consistency}.

{\bf Summary of results of this paper} Notation and assumptions pertaining to this summary are defined in the problem setup section below. We prove under broad conditions that the excess risk of the Hilbert regression estimator is asymptotically equivalent pointwise to $\sigma^2(x)/\ln(n)$ where $\sigma^2(x)$ is the noise variance. We also show that the excess risk of the plugin classifier is upper bounded by
$2|f(x)-1/2|^{1-\alpha}\,(1+\varepsilon)^\alpha \sigma^\alpha(x)(\ln(n))^{-\frac{\alpha}{2}}$,
for any $0<\alpha<1$, where $f$ is the regression function $x\mapsto\mathbb{E}[y|x]$. Our proofs proceed by deriving asymptotic equivalents of the moments of the weight functions $w_i(x)$ for large $n$, for instance for $\beta>1$, $\mathbb{E}[w_i^{\beta}(x)]\sim_{n\rightarrow \infty}((\beta-1)n\ln(n))^{-1}$.  We further derive an asymptotic equivalent for the Lagrange function and explicitly exhibit the nontrivial extrapolation properties of this estimator. Notably, the convergence rates are independent of data dimension and the excess risk is dominated by the noise variance. The bias term, for which we also give precise asymptotic estimates, is always subleading when the density of data at the considered point is strictly positive. If this local density is zero, we show that the bias term does not vanish in the limit of a large data set and we compute its limit explicitly.
Finally, we  present heuristic arguments for a universal $w^{-2}$ power-law behavior of the probability density of the weights in the large $n$ limit.

\section{Problem setup}

{\bf Notation, Definitions, Statistical Model} We model the labelled training data set $(x_0,y_0),\dotsc,(x_n,y_n)$ as $n+1$ {\it i.i.d.} observations of a random vector $(X,Y)$ with values in $\R^d \times \R$ for regression, and with values in $\R^d \times \{0,1\}$ for binary classification. Due to the independence property, the collection $X_0,\dotsc,X_n$ has the product density $\prod_{i=0}^n\rho(x_i)$. We will denote by $\E$ an expectation over the collection of $n+1$ random vectors and by $\E_X$ the expectation over the collection $X_0,\dotsc,X_n$. An expectation over the same collection while holding $X_i=x_i$ will be denoted $\E_{X|x_i}$.
The regression function $f \colon \R^d \to \R$ is defined as the conditional mean of $Y$ given $X=x$, $f(x) := \E[Y \mid X = x]$ and the conditional variance function is $\sigma^2(x):=\E[|Y-f(X)|^2|X=x]$. $f$ minimizes the expected value of the mean squared prediction error (risk under squared loss), $f = \argmin \mse(h)$ where $\mse(h) := \E[(h(X) - Y)^2]$. Given any regression estimator $\hat{f}(x)$ the corresponding risk can be decomposed as $\E[\mse(\hat{f}(X))] = \mse(f) + \E[ (\hat{f}(X) - f(X)^2]$. The excess risk is given by $\mse(\hat{f})-\mse(f) = \E[(\hat{f}(X) - f(X))^2]$. For a consistent estimator this excess risk goes to zero as $n\rightarrow \infty$ and we are interested in characterizing the {\it rate} at which it goes to zero with increasing $n$ (note our sample size is $n+1$ for notational simplicity but for large $n$ this does not change the rate).

In the case of binary classification, $Y\in \{0,1\}$ and $f(x) = \P[Y=1 \mid X=x)]$. Let $F \colon \R^d \to \{0,1\}$ denote the Bayes optimal classifier, defined by $F(x) := \theta(f(x) - 1/2)$ where $\theta(\cdot)$ is the Heaviside theta function. This classifier minimizes the risk $\risk(h) := \E[\ind{h(X) \neq Y}] = \P(h(X) \neq Y)$ under zero-one loss. Given the regression estimator $\hat{f}$, we consider the plugin classifier $\hat{F} (x)=\theta(\hat f(x)-\frac{1}{2})$. The classification risk for the plugin classifier $\hat{F}$ is bounded as $\E[\risk(\hat F(x))] - \risk(F(x)) \leq 2\E[|\hat f(x) - f(x)|]\leq 2\sqrt{\E[(\hat{f}(x)-f(x))^2]}$.

Finally, we define two sequences $a_n,b_n>0$, $n\in\N$, to be asymptotically equivalent for $n\to+\infty$, denoted $a_n\sim_{n\to+\infty} b_n$, if the limit of their ratio exists and  $\lim_{n\to\infty} a_n/b_n = 1$.

In summary, our work will focus on the estimation of asymptotic equivalents for $\E[(\hat{f}(x)-f(x))^2]$ and other relevant quantities as this determines the rate at which the excess risk goes to zero for regression, and bounds the rate at which the excess risk goes to zero for classification.

\noindent{}{\bf Assumptions.} We define the support $\Omega$ of  the density $\rho$ as $\Omega=\{x\in \R^d /\rho(x)>0\}$, the closed support $\bar\Omega$ as the closure of $\Omega$, and $\Omega^\circ$ as the interior of $\Omega$. Our results will not assume any compactness condition on $\Omega$ or $\bar\Omega$. The boundary of $\Omega$ is then defined as $\partial\Omega=\bar\Omega\setminus\Omega^\circ$. We assume that $\rho$ has a finite variance $\sigma_\rho^2$. In addition, we will most of the time assume that the density $\rho$ is continuous at the considered point $x\in \Omega^\circ$, and in some cases,  $x\in \partial\Omega\cap\Omega$.

For the regression function $f$, we will obtain results assuming either of the following conditions
\begin{itemize}
\item $C_{\rm Cont}^f$: $f$ is continuous at the considered $x$,
\item $C_{\rm Holder}^f$: for all $x\in\Omega^\circ$, there exist $\alpha_x>0$, $K_x>0$, and $\delta_x>0$, such that  \\
$x'\in\Omega$ and  $\|x-x'\|\leq \delta_x\implies |f(x) - f(x')| \leq K_x\,\|x-x'\|^{\alpha_x}$ \\(local H\"older smoothness condition),
\end{itemize}
where condition $C_{\rm Holder}^f$ is obviously stronger than $C_{\rm Cont}^f$.
In addition, we will always assume a growth condition  for the regression function $f$:
\begin{itemize}
\item $C_{\rm Growth}^f$: $\int \rho(y)\frac{f^2(y)}{1+\|y\|^{2d}}\,d^dy<\infty$.
\end{itemize}

As for the variance function $\sigma$, we will obtain results assuming either that $\sigma$ is bounded or satisfies a growth condition similar to the one above
\begin{itemize}
\item $C_{\rm Bound}^\sigma$: there exists $\sigma_0^2\geq 0$, such that, for all $x\in \Omega$, we have $\sigma^2(x)\leq\sigma_0^2$,
\item $C_{\rm Growth}^\sigma$: $\int \rho(y)\frac{\sigma^2(y)}{1+\|y\|^{2d}}\,d^dy<\infty$.
\end{itemize}
When we will assume condition $C_{\rm Growth}^\sigma$ (obviously satisfied when  $\sigma^2$ is bounded), we will also assume a continuity condition $C_{\rm Cont}^\sigma$ for $\sigma$ at the considered $x$.

Note that all our results can be readily extended in the case where  $x\in \partial\Omega=\bar\Omega\setminus\Omega^\circ$ but keeping the condition  $\rho(x)>0$ (i.e., $x\in\partial\Omega\cap\Omega$), and assuming the continuity at $x$ of $\rho$ as seen as a function restricted to $\Omega$, i.e., $\lim_{y\in \Omega\to x}\rho(y)=\rho(x)$. Useful examples are when the support $\Omega$ of $\rho$ is a $d$-dimensional sphere or hypercube and $x$ is on the surface of $\Omega$  (but still with $\rho(x)>0$). To guarantee these results for $x\in \partial\Omega\cap\Omega$, we need also to assume the continuity at $x$ of $f$, and assume that $\Omega$ is smooth enough near $x$, so that there exists a strictly positive local solid angle $\omega_x$ defined by
\begin{equation}
\omega_x=    \lim_{r\to 0}\frac{1}{V_d\rho(x)r^d}\int_{\|x-y\|\leq r}\rho(y)\,d^dy=
\lim_{r\to 0}\frac{1}{V_dr^d}\int_{y\in\Omega/\|x-y\|\leq r}\,d^dy,
\end{equation}
where $V_d=S_d/d=\pi^{d/2}/\Gamma(d/2+1)$ is the volume of the unit ball in $d$ dimensions, and the second inequality results from the continuity of $\rho$ at $x$.
If $x\in \Omega^\circ$, we have $\omega_x=1$, while for $x\in \partial\Omega$, we have $0\leq \omega_x\leq 1$. For instance, if $x$ is on the surface of a sphere or on the interior of a face of a hypercube (and in general, when the boundary near $x$ is locally an hyperplane), we have $\omega_x=\frac{1}{2}$. If $x$ is a corner of a hypercube, we have  $\omega_x=\frac{1}{2^d}$. From our methods of proof presented in the appendix, it should be clear that all our results for $x\in \Omega^\circ$ perfectly generalize to any $x\in \partial\Omega\cap\Omega$ for which $\omega_x>0$, by simply replacing $V_d$ whenever it appears in our different results by $\omega_x V_d$.

\vskip 0.2cm
{\bf Hilbert kernel interpolating estimator and Bias-Variance decomposition.} The Hilbert kernel regression estimator $\hat{f}(x)$ is a Nadaraya-Watson style estimator employing a singular kernel:
\begin{eqnarray}
    w_i(x) &=& \frac{\|x-x_i\|^{-d}}{\sum_{j=0}^n \|x-x_j\|^{-d}}, \\
    \hat{f}(x) &=& \sum_{i=0}^n w_i(x)y_i.
\end{eqnarray}
The weights $w_i(x)$ are also called Lagrange functions in the interpolation literature and satisfy the interpolation property $w_i(x_j)=\delta_{ij}$, where  $\delta_{ij}=1$, if $i=j$, and 0 otherwise. At any given point $x$, they provide a partition of unity so that $\sum_{i=0}^n w_i(x)=1$. The mean squared error between the Hilbert estimator and the true regression function has a bias-variance decomposition (using the {\it i.i.d} condition and the earlier definitions)
\begin{eqnarray}
     \hat{f}(x)-f(x) &=& \sum_{i=0}^n w_i(x)[f(x_i)-f(x)] + \sum_{i=0}^n w_i(x)[y_i-f(x_i)],\\
    \E[(\hat{f}(x)-f(x))^2] &=& {\cal B}(x) + {\cal V}(x), \\
    (Bias)~~{\cal B}(x)&=& \E_X\Bigl[\Bigl(\sum_{i=0}^n w_i(x) [f(x_i)-f(x)]\Bigr)^2\Bigr],\\
    (Variance)~~{\cal V}(x)&=& \E\Bigl[\sum_{i=0}^n w_i^2(x) [y_i-f(x_i)]^2\Bigr] = \E_X\Bigl[\sum_{i=0}^n w_i^2(x) \sigma^2(x_i) \Bigr].\\
    \nonumber
\end{eqnarray}

The present work derives asymptotic behaviors and bounds for the regression and classification risk of the Hilbert estimator for large sample size $n$. These results are derived by analyzing the large $n$ behaviors of the bias and variance terms, which in turn depend on the behavior of the moments of the weights or the Lagrange functions $w_i(x)$. For all these quantities, asymptotically equivalent forms are derived. The proofs exploit a simple integral form of the weight function and details are provided in the appendix, while the body of the paper provides the results and associated discussions.

\section{Results}

\subsection{The weights, variance and bias terms}

\subsubsection{Moments of the weights: large $n$ behavior}
\label{subsubsection:weights}
In this section, we consider the moments and the distribution of the weights $w_i(x)$ at a given point $x$. The first moment is simple to compute. Since the weights sum to 1 and $X_i$ are {\it i.i.d}, it follows that $\E_{X|x_i}[w_i(x)]$ are all equal and thus
$\E_{X|x_i}[w_i(x)]=(n+1)^{-1}$. The other moments are much less trivial to compute and we prove the following theorem in the appendix~\ref{prooftheo1}:

\begin{theorem}\label{theo1}
For $x\in\Omega^\circ$ (so that $\rho(x)>0$),  we assume $\rho$ continuous at $x$. Then, the moments of the weight $w_0(x)$ satisfy the following properties:
\begin{itemize}
    \item For $\beta>1$:
\begin{equation}
    \E\left[w_0^\beta(x)\right]\underset{n\to +\infty  }{\sim}\frac{1}{(\beta-1) n\ln(n)}.
\end{equation}
\item For \,$0<\beta<1$: \,defining
$	\kappa_\beta(x):=\int \frac{\rho(x+y)}{||y||^{\beta d}}\,d^dy<\infty$,
we have
\begin{eqnarray}\label{eqbeta1}
\E\left[w_0^\beta(x)\right]\underset{n\to +\infty  }{\sim}\frac{\kappa_\beta(x)}{(V_d\rho(x) n\ln(n))^\beta}.
\end{eqnarray}
\item For $\beta<0$: \,all moments for  $\beta\leq -1$ are infinite, and the moments of order $-1<\beta<0$ satisfy
\begin{equation}
\E\left[w_0^\beta(x)\right]\leq 1+n\,\kappa_{|\beta|}(x)\kappa_{\beta}(x),
\end{equation}
so that a sufficient condition for its existence is $\kappa_{\beta}(x)=\int {\rho(x+y)}{||y||^{|\beta|d}}\,d^dy<\infty$.
\end{itemize}
\end{theorem}

Heuristically, the behavior of these moments are consistent with  the random variable $W=w_0(x)$ having a probability distribution satisfying a scaling relation $P(W)=\frac{1}{W_n} p\left(\frac{W}{W_n} \right)$, with the scaling function $p$ having the universal tail (i.e., independent of $x$ and $\rho$),  $p(w)\underset{w\to +\infty  }{\sim}w^{-2}$, and a scale $W_n$ expected to vanish with $n$, when $n\to+\infty$. With this assumption, we can determine the scale $W_n$ by imposing the exact condition $\E[W]=1/(n+1)\sim 1/n$:
\begin{eqnarray}
\E[W]&=&\frac{1}{W_n}\int_0^1 p\left(\frac{W}{W_n} \right)W\,dW=W_n \int_0^{\frac{1}{W_n}}p(w)w\,dw\\
&\sim& W_n\int_1^{\frac{1}{W_n}} \frac{dw}{w}  \sim-W_n \ln(W_n)\sim \frac{1}{n},
\end{eqnarray}
leading to $W_n\sim \frac{1}{n\ln(n)}$. Then, the moment of order $\beta>1$ is given by
\begin{equation}\label{heuri1}
	\E[W^{\beta}]=\frac{1}{W_n}\int_0^1 p\left(\frac{W}{W_n} \right)W^{\beta}\,dW\sim W_n\int_0^1W^{\beta-2}\,dW
	\underset{n\to +\infty  }{\sim}\frac{1}{(\beta-1) n\ln(n)},
\end{equation}
which indeed coincides with the first result of  Theorem~\ref{theo1}.
Our heuristic argument also suggests that in the case $0<\beta<1$, we have
\begin{eqnarray}
	\E[W]=\frac{1}{W_n}\int_0^1 p\left(\frac{W}{W_n} \right)W^{\beta}\,dW
	&\underset{n\to +\infty}{\sim}& \frac{\int_0^{+\infty} p\left(w \right)w^\beta \,dw}{(n\ln(n))^\beta} ,\label{heuri2}
\end{eqnarray}
where the last integral converges since $p(w)\underset{w\to +\infty  }{\sim}w^{-2}$ and $\beta<1$. This result is perfectly consistent with \eq{eqbeta1} in Theorem~\ref{theo1}, and suggests that $\int_0^{+\infty} p\left(w \right)w^\beta \,dw=\frac{\kappa_\beta(x)}{(V_d\rho(x))^\beta}$. Interestingly, for $0<\beta<1$, and contrary to the case $\beta>1$, we find that the large $n$ equivalent of the moment is not universal and depends explicitly on $x$ and the density $\rho$.
As for moments of order $-1<\beta<0$, we conjecture that they are still given by \eq{eqbeta1} (and equivalently, by \eq{heuri2}) provided they exist, and that the sufficient condition  for their existence $\kappa_{\beta}(x)<\infty$ is hence also necessary, since $\kappa_{\beta}(x)$ also appears in \eq{eqbeta1}. The fact that moments for $\beta\leq -1$ do not exist strongly suggests that $p(0)>0$. In fact, \eq{heuri2}) also suggests that all moments for $-1<\beta<0$ exist if and only if  $0<p(0)<\infty$. In the Fig.~\ref{figdist} of the appendix, we present numerical simulations confirming our scaling ansatz, the fact that $p(w)\underset{w\to +\infty  }{\sim}w^{-2}$, and the quantitative prediction for $W_n$.

It is shown in Devroye {\it et al.}~\cite{devroye1998hilbert} that the Hilbert kernel regression estimate does not converge almost surely ({\it a.s.}) by giving a specific example. Insight can be gained into this lack of almost sure convergence by considering the weight function $w_0(x)$, for a sequence of independent training sample sets of increasing size $n+1$.
Let the corresponding sequence of weights be denoted as $\omega_n\in[0,1]$. From Theorem~\ref{theo1}, it is clear that  $\omega_n$ converges to zero in probability, since the following Chebyshev bound holds (analogous to the bound on the regression risk):
\begin{equation}\label{omegan}
    \P(\omega_n>\varepsilon)\leq \frac{1+\delta}{\varepsilon^2n\ln(n)},
\end{equation}
for arbitrary $\varepsilon>0$ and $\delta>0$, and for $n$ larger than some constant $N_{x,\delta}$. Alternatively, one can exploit the fact that $\E[\omega_n]=\frac{1}{n+1}$, leading to
$\P(\omega_n>\varepsilon)\leq \frac{1}{\varepsilon\,  n}$,
which is less stringent than \eq{omegan} as far as the $n$-dependence is concerned, but is more stringent for the  $\varepsilon$-dependence of the bounds.

Let us show  heuristically that $\omega_n$ does not converge {\it a.s.} to zero. Consider the infinite sequence of events ${\cal E}_n\equiv \{\omega_n>\varepsilon\}$, $n\in \N$, and the corresponding infinite sum $\sum_n\P({\cal E}_n) = \sum_n\P(\omega_n>\varepsilon)$. Exploiting our previous heuristic argument for the scaling form of the distribution of weights, we obtain
\begin{equation}
    \P(\omega_n>\varepsilon)=\int_{\varepsilon}^1 \frac{1}{W_n}p\left(\frac{W}{W_n}\right)\, dW\sim \int_{\varepsilon\,  n\ln n}^{n\ln n} \frac{d w}{w^2} \sim \frac{1-\varepsilon}{\varepsilon\, n\ln(n)}.
\end{equation}
Since $\sum_{n=2}^{N} \frac{1}{n\ln (n)}\sim\ln(\ln(N))$ is a divergent series, a Borel-Cantelli argument  suggests that an infinite number of the events ${\cal E}_n$ (i.e., $\omega_n>\varepsilon$) must occur, which implies that $\omega_n$ does not converge {\it a.s.} to 0.
Note that the weights are equal to 1 at the data points due to the interpolation condition, so that large weights occasionally occur, causing the lack of {\it a.s.} convergence.

\subsubsection{Lagrange function: scaling limit}

The expected value of the Lagrange functions $w_i(x)$ have a simple form in the large $n$ limit. Due to the {\it i.i.d.} condition the indices $i$ are exchangeable and we set $i=0$ for the computation of the expected Lagrange function $L_0(x)=\E_{X|x_0} [w_0(x)]$. Thus, one of the sample points (denoted $x_0$) is held fixed and the other ones are averaged over in computing the expected Lagrange function.
For $x_0\ne x$ kept fixed, we  have $\lim_{n\rightarrow \infty}L_0(x)= 0$. However, we show in the appendix~\ref{prooflag}  that $L_0(x)$ takes a very simple form when taking a specific scaling limit:

\begin{theorem}
\label{theolag}
For $x\in\Omega^\circ$, we assume $\rho$ continuous at $x$.
Then, in the limit
(denoted by $\lim_Z$), $n\to+\infty$, $\|x-x_0\|^{-d}\to +\infty$  (i.e., $x_0\to x$), and such that $z_x(n,x_0)=V_d\rho(x)\|x-x_0\|^d n\log(n)\to Z$, the Lagrange function $L_0(x)=\E_{X|x_0} [w_0(x)]$ converges to a proper limit,
\begin{equation}
    \lim_{Z} L_0(x)= \frac{1}{1+Z}.
\end{equation}
\end{theorem}

The proof of this theorem shows that  the relative error between $L_0(x)$ and $\frac{1}{1+Z}$ for finite but large $n$ and large $\|x-x_0\|^{-d}$, such that  $z_x(n,x_0)$ remains close to $Z$, is  $O(1/\ln(n))$.

Exploiting Theorem~\ref{theolag}, we can use a simple heuristic argument to estimate the tail of the distribution of the random variable $W=w_0(x)$.
Indeed, approximating  $L_0(x)$ for finite but large $n$ by its asymptotic form $\frac{1}{1+z_x(n,x_0)}$, with $z_x(n,x_0)=V_d\rho(x) n\log(n)\|x-x_0\|^d$, we obtain
\begin{eqnarray}
\int_W^{1}P(W')\,dW' &\sim&\int \rho(x_0)\,\theta\left(\frac{1}{1+V_d\rho(x) n\log(n)\|x-x_0\|^d}-W\right)\,d^dx_0,\\
    &\sim& V_d\rho(x)\int_0^{+\infty} \theta\left(\frac{1}{1+V_d\rho(x) n\log(n)\, u}-W\right)\,du,\\
    &\sim& \frac{1}{n\ln(n)W}\quad\implies   P(W)\sim \frac{1}{n\ln(n)W^2},\label{argtail}
\end{eqnarray}
where $\theta(.)$ is the Heaviside function.
This heuristic result is again perfectly consistent with our guess of the previous section that  $P(W)=\frac{1}{W_n} p\left(\frac{W}{W_n} \right)$, with the scaling function $p$ having the universal tail,  $p(w)\underset{w\to +\infty  }{\sim}w^{-2}$, and a scale $W_n\sim \frac{1}{n\ln(n)}$. Indeed, in this case and in the limit $n\to+\infty$, we  obtain that  $P(W)\sim\frac{1}{W_n}\left(\frac{W_n}{W}\right)^2\sim\frac{W_n}{W^2}\sim \frac{1}{n\ln(n)W^2}$, which is identical to the result of \eq{argtail}.

\subsubsection{The variance term}

A simple application of the result of Theorem~\ref{theo1} for $\beta=2$  (see appendix~\ref{proofvar}) allows us to bound the variance term ${\cal V}(x)=\E\Bigl[\sum_{i=0}^n w_i^2(x) [y_i-f(x_i)]^2\Bigr]$ for a bounded variance function $\sigma^2$:
\begin{theorem}\label{theovar1}
For $x\in\Omega^\circ$, $\rho$ continuous at $x$,  $\sigma^2\leq\sigma_0^2$, and for any $\varepsilon>0$,
there exists a constant $N_{x,\varepsilon}$ such that for $n\geq N_{x,\varepsilon}$, we have
\begin{equation}
   {\cal V}(x)\leq (1+\varepsilon)\frac{\sigma_0^2}{\ln(n)}.
\end{equation}
\end{theorem}

Relaxing the boundedness condition for $\sigma$, but assuming the continuity of $\sigma^2$ at $x$ along with a growth condition, allows us to obtain a precise asymptotic equivalent of ${\cal V}(x)$, when $n\to+\infty$:

\begin{theorem}\label{theovar2}
For $x\in\Omega^\circ$, $\sigma(x)>0$, $\rho\sigma^2$ continuous at $x$,  and assuming the condition $C_{\rm Growth}^\sigma$, i.e., $\int \rho(y)\frac{\sigma^2(y)}{1+\|y\|^{2d}}\,d^dy<\infty$, we have
\begin{equation}
   {\cal V}(x)\underset{n\to +\infty  }{\sim}\frac{\sigma^2(x)}{\ln(n)}.
\end{equation}
\end{theorem}

Note  that if the mean variance  $\int \rho(y)\sigma^2(y)\,d^dy<\infty$, which is in particular the case when $\sigma^2$ is bounded over $\Omega$, then the condition $C_{\rm Growth}^\sigma$ is in fact automatically satisfied.

\subsubsection{The bias term}

In appendix~\ref{proofbias}, we prove the following three theorems for the bias term.
\begin{theorem}\label{theobias}
For $x\in\Omega^\circ$ (so that $\rho(x)>0$), we assume that  $\rho$ is continuous at $x$,  and the conditions
\begin{itemize}
\item $C_{\rm Growth}^f$: $\int \rho(y)\frac{f^2(y)}{1+\|y\|^{2d}}\,d^dy<\infty$,
\item $C_{\rm Holder}^f$: there exist $\alpha_x>0$, $K_x>0$, and $\delta_x>0$, such that  \\$x'\in\Omega$ and  $\|x-x'\|\leq \delta_x\implies |f(x) - f(x')| \leq K_x\,\|x-x'\|^{\alpha_x}$ \\(local Hölder condition for $f$).
\end{itemize}
Moreover, we define $\kappa(x)= \int \rho(x+y)\frac{f(x+y)-f(x)}{||y||^{d}}\,d^dy$, where we have $|\kappa(x)|<\infty$.

Then, for $\kappa(x)\neq 0$, the bias term ${\cal B}(x)= \E_X\Bigl[\Bigl(\sum_{i=0}^n w_i(x) [f(x_i)-f(x)]\Bigr)^2\Bigr]$ satisfies
\begin{eqnarray}\label{biaskne0}
    {\cal B}(x)\underset{n\to +\infty }{\sim}\left(\E\left[\hat f(x)\right]-f(x)\right)^2,
 \qquad {\rm with}\quad  \E\left[\hat f(x)\right]-f(x) \underset{n\to +\infty  }{\sim}\frac{\kappa(x)}{V_d\rho(x)\ln(n)}.\label{limefhat}
\end{eqnarray}
In the non generic case $\kappa(x)=0$, we  have the weaker result
\begin{equation}\label{Bcasetheo}
{\cal B}(x)=\left\{\begin{array}{lr}
        O\left(n^{-\frac{2\alpha_x}{d}}(\ln(n))^{-1-\frac{2\alpha_x}{d}}\right), & \text{for }\, d>2\alpha_x\vspace{0.25cm}\\
       O\left(n^{-1}(\ln(n))^{-1}\right), & \text{for }\,d=2\alpha_x\vspace{0.35cm}\\
        O\left(n^{-1}(\ln(n))^{-2}\right), & \text{for }\, d<2\alpha_x
        \end{array}\right.
\end{equation}
\end{theorem}

Note that $\kappa(x)=0$ is non generic but can still happen, even if $f$ is not constant. For instance, if $\Omega$ is a sphere centered at $x$ or $\,\Omega=\R^d$, if $\rho(x+y)=\hat\rho(||y||)$ is isotropic around $x$, and if $f_x:y\mapsto f(x+y)$ is an odd function of $y$, then we indeed have $\kappa(x)=0$ at this symmetric point $x$.

Interestingly, for $\kappa(x)\neq 0$, \eq{biaskne0} shows that the bias ${\cal B}(x)$ is asymptotically dominated by the square of $\E\left[\hat f(x)\right] - f(x)$, showing that the fluctuations of $\E\left[\hat f(x)\right]-\sum_{i=0}^n w_i(x) f(x_i)$ are negligible compared to $\E\left[\hat f(x)\right]-f(x)$, in the limit $n\to+\infty$ and for $\kappa(x)\neq 0$.

One can relax the local Hölder condition, but at the price of a weaker estimate for ${\cal B}(x)$ which will however be enough to obtain strong results for the regression and classification risks (see below):

\begin{theorem}\label{theobiasbis}
For $x\in\Omega^\circ$, we assume  $\rho$ and $f$ continuous at $x$,  and the growth condition $C_{\rm Growth}^f$: $\int \rho(y)\frac{f^2(y)}{1+\|y\|^{2d}}\,d^dy<\infty$. Then, the bias term satisfies
\begin{equation}
    {\cal B}(x)=o\left( \frac{1}{\ln(n)}\right),
\end{equation}
or equivalently, for any $\varepsilon>0$, there exists  $N_{x,\varepsilon}$, such that for $n\geq N_{x,\varepsilon}$
\begin{equation}
    {\cal B}(x)\leq  \frac{\varepsilon}{\ln(n)}.
\end{equation}
\end{theorem}

Let us now consider a point $x\in\partial\Omega$ for which we have $\rho(x)=0$ (note that $x\in\partial\Omega$ does not necessarily imply $\rho(x)=0$).
In appendix~\ref{proofbias}, we show the following theorem for the expectation value of the estimator $\hat f(x)$ in the limit $n\to+\infty$:

\begin{theorem}\label{theorhonon0}
For $x\in\partial\Omega$ such  that $\rho(x)=0$, we assume that $f$ and $\rho$ satisfy the conditions
\begin{itemize}
\item $C_{\rm Growth}^f$: $\int \rho(y)\frac{|f(y)|}{1+\|y\|^{d}}\,d^dy<\infty$,
\item $C_{\rm Holder}^\rho$: there exist $\alpha_x>0$, $K_x>0$, and $\delta_x>0$, such that  \\$x'\in\Omega$ and  $\|x-x'\|\leq \delta_x\implies |\rho(x')| \leq K_x\,\|x-x'\|^{\alpha_x}$ \\(local Hölder condition for $\rho$).
\end{itemize}
Moreover, we define $\kappa(x)= \int \rho(x+y)\frac{f(x+y)-f(x)}{||y||^{d}}\,d^dy$ ~($|\kappa(x)|<\infty$ under condition $C_{\rm Growth}^f$), and
$\lambda(x)= \int \frac{\rho(x+y)}{||y||^{d}}\,d^dy$ ~($0<\lambda(x)<\infty$ under condition $C_{\rm Holder}^\sigma$).
Then,
\begin{eqnarray}
   \lim_{n\to+\infty}\E[\hat f(x)]-f(x)=
   \frac{\kappa(x)}{\lambda(x)}.
\end{eqnarray}
\end{theorem}

Hence, in the generic case $\kappa(x)\ne 0$ (see Theorem~\ref{theobias} and the discussion below it) and under condition $C_{\rm Holder}^\rho$, we find that the bias does not vanish when $\rho(x)=0$, and that the estimator $\hat f(x)$ does not converge to $f(x)$. When $\rho(x)=0$, the scarcity of data near the point $x$ indeed prevents the estimator to converge to the actual value of $f(x)$. In appendix~\ref{proofbias}, we show an example of a  density $\rho$ continuous at $x$ and such that $\rho(x)=0$, but not satisfying the condition $C_{\rm Holder}^\rho$, and for which  $\lim_{n\to+\infty}\E[\hat f(x)]=f(x)$, even if $\kappa(x)\neq 0$.

\subsection{Asymptotic equivalent for the regression risk}

In appendix~\ref{prooftheorisk}, we prove the following theorem establishing the asymptotic rate at which the excess risk goes to zero with large sample size $n$ for Hilbert kernel regression, under mild conditions that do not require  $f$ or $\sigma$ to be bounded, but only to satisfy some growth conditions:

\begin{theorem}
\label{regressionrisk}
For $x\in\Omega^\circ$, we assume $\sigma(x)>0$, $\rho$,  $\sigma$, and $f$ continuous at $x$,  and the growth conditions~
$C_{\rm Growth}^\sigma$: $\int \rho(y)\frac{\sigma^2(y)}{1+\|y\|^{2d}}\,d^dy<\infty$ ~and~
$C_{\rm Growth}^f$: $\int \rho(y)\frac{f^2(y)}{1+\|y\|^{2d}}\,d^dy<\infty$.

Then the following statements are true:
\begin{itemize}
    \item The excess regression risk at the point $x$  satisfies
\begin{equation}
    \E[(\hat{f}(x)-f(x))^2]\underset{n\to +\infty  }{\sim} \frac{\sigma^2(x)}{\ln(n)}.
\end{equation}

\item The Hilbert kernel estimate converges pointwise to the regression function in probability. \\More specifically, for any $\delta>0$, there exists a constant $N_{x,\delta}$, such that  for any $\varepsilon>0$, we have the following  Chebyshev bound, valid for $n\geq N_{x,\delta}$
\begin{equation}
\P[|\hat{f}(x)-f(x)| \geq \varepsilon]\leq \frac{1+\delta}{\varepsilon^2}\, \frac{\sigma^2(x)}{\ln(n)}.
\end{equation}
\end{itemize}

\end{theorem}

This theorem is a  consequence of the corresponding asymptotically equivalent forms of the variance and bias terms presented above. Note that as long as $\rho(x)>0$, the variance term dominates over the bias term and the regression risk has the same form as the variance term.

\subsection{Rates for the plugin classifier}
In appendix~\ref{proofclassrisk}, we prove the following theorem establishing the asymptotic rate at which the classification risk goes to zero with large sample size $n$ for Hilbert kernel regression:
\begin{theorem}
\label{theoclass}
For $x\in\Omega^\circ$, we assume $\sigma(x)>0$, $\rho$, $\sigma$, and  $f$ continuous at $x$. Then, the classification   risk $\E[\risk(\hat F(x))] - \risk(F(x))$ vanishes for $n\to+\infty$.

More precisely, for any $\varepsilon>0$, there exists $N_{x,\varepsilon}$, such that for any $n\geq  N_{x,\varepsilon}$,
\begin{equation}\label{alpha0risk}
    0\leq \E[\risk(\hat F(x))] - \risk(F(x)) \leq 2(1+\varepsilon) \frac{\sigma(x)}{\sqrt{\ln(n)}},\\
\end{equation}

In addition, for any  $0<\alpha<1$, the general inequality
\begin{equation}
\E[\risk(\hat F(x))] - \risk(F(x)) \leq 2|f(x)-1/2|^{1-\alpha}\, {\E\left[|\hat f(x) - f(x)|^{2}\right]^\frac{\alpha}{2}},
\end{equation}
holds unconditionally and, for $n\geq  N_{x,\varepsilon}$, leads to
\begin{equation}\label{alpharisk}
0\leq \E[\risk(\hat F(x))] - \risk(F(x)) \leq 2|f(x)-1/2|^{1-\alpha}\,(1+\varepsilon)^\alpha\frac{\sigma^\alpha(x)}{(\ln(n))^\frac{\alpha}{2}}.
\end{equation}
\end{theorem}

For  $0<\alpha<1$, \eq{alpharisk} is weaker than \eq{alpha0risk} in terms of its dependence on $n$, but explicitly shows that the classification  risk vanishes for $f(x)=1/2$. This theorem does not require any growth condition for $f$ or $\sigma$, since both functions takes values in $[0,1]$ in the classification context.

\subsection{Extrapolation behavior outside the support of $\rho$}

We now take the point $x$ outside the closed support $\bar\Omega$ of the distribution $\rho$ (which excludes the case  $\Omega=\R^d$). We are interested in the behavior of $\E\left[\hat f(x)\right]$ as $n\to+\infty$. In  appendix~\ref{proofout} we prove:
\begin{theorem}
\label{theoout}
For $x\notin\bar\Omega$, we assume the growth condition $\int \rho(y)\frac{|f(y)|}{1+\|y\|^{d}}\,d^dy<\infty$. Then,
\begin{equation}
\hat f_\infty(x):=\lim_{n\to+\infty} \E\left[\hat f(x)\right]=\frac{\int{\rho(y)f(y)\|x-y\|^{-d}} \,d^dy}{\int\rho(y)\|x-y\|^{-d} \,d^dy},
\end{equation}
and $\hat f_\infty$ is continuous at all  $x\notin\bar\Omega$.

In addition, if  $\int\rho(y)|f(y)|\,d^dy<\infty$, and defining $d(x,\Omega)>0$ as the distance between $x$ and $\Omega$, we have
\begin{equation}\label{larged}
\lim_{d(x,\Omega)\to+\infty}\hat  f_\infty(x)=\int\rho(y)f(y)\,d^dy.
\end{equation}
Finally, we consider $x_0\in\partial \Omega$ such that  $\rho(x_0)>0$ (i.e., $x_0\in \partial \Omega\cap\Omega$), and  assume that $f$ and $\rho$ seen as functions restricted to $\Omega$ are continuous at $x_0$, i.e. $\lim_{y\in\Omega\to x_0} \rho(y)=\rho(x_0)$ and $\lim_{y\in\Omega\to x_0} f(y)=f(x_0)$. We also assume  that the local solid angle  $\omega_0=\lim_{r\to 0}\frac{1}{V_d\rho(x_0)r^d}\int_{\|x_0-y\|\leq r}\rho(y)\,d^dy$   exists and satisfies $\omega_0>0$.
 Then,
\begin{equation}\label{contfinf}
\lim_{x\notin \bar\Omega\to x_0}\hat f_\infty(x)=f(x_0).
\end{equation}
\end{theorem}

\eq{larged} shows that far away from $\Omega$ (which is possible to realize, for instance, when $\Omega$ is bounded), $\hat f_\infty(x)$ goes smoothly to the $\rho$-mean of $f$. Moreover,  \eq{contfinf} establishes a continuity property for the extrapolation $\hat f_\infty$ at $x_0\in\partial \Omega\cap\Omega$ under the stated conditions (remember that for $x\in \Omega^\circ$,  we have $\lim_{n\to+\infty} \E\left[\hat f(x)\right]=f(x)$; see Theorem~\ref{theobias}, and in particular \eq{limefhat}).

\section*{Acknowledgements}

PPM gratefully acknowledges the support of the Crick-Clay Professorship (CSHL) and the H N Mahabala Chair (IITM).

redpajama_set_name: RedPajamaArXiv


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> Criminalizing Dissent
> Discriminatory Policing
The Nation v. Haig
The Nation v. Haig was a case which defended the right of Americans to receive Cuban publications.
United States v. Ahmed Abdel Sattar, et al. (amicus)
United States v. Ahmed Abdel Sattar, et al. is a case in which Lynne Stewart, a criminal defense attorney who represented Sheikh Abdel Rahman, was indicted on April 9, 2002, for providing "material...
Detroit Free Press (Haddad) v. Creppy and Ashcroft/North Jersey Media Group v. Creppy and Ashcroft
Detroit Free Press (Haddad) v. Creppy and Ashcroft/North Jersey Media Group v. Creppy and Ashcroft is a civil rights case challenging the government's attempt to close immigration hearings in cases...
United States v. Dellinger
United States v. Dellinger is a criminal case in which the Center for Constitutional Rights (CCR) challenged the Justice Department's misuse of the grand jury process in conducting its investigation...
United States v. Berkan
United States v. Berkan is a criminal case in which the Center for Constitutional Rights (CCR) represented Judy Berkan, Bishop Antulio Parilla Bonilla, Salvador Tió, and William Andrés Trevathan and...
United States v. Banks and Means (Wounded Knee)
United States v. Banks and Means is a 1974 case in which the Center for Constitutional Rights (CCR) defended American Indian sovereignty at Wounded Knee and represented leaders in the American Indian...
United States v. Brett Bursey
United States v. Brett Bursey is an appeal brief filed by the Center for Constitutional Rights (CCR) and cooperating attorney Lewis Pitts, charging that the Secret Service violated its own...
Taylor v. Hayes
Taylor v. Hayes is a civil case that went up to the Supreme Court in which the Center for Constitutional Rights (CCR) contested Kentucky attorney Dan Taylor's four-and-a half-year jail sentence for...
State of Washington v. Wanrow
State of Washington v. Wanrow is a lawsuit that challenged the murder conviction of Yvonne Swan Wanrow on the grounds of a woman's right to self-defense against harm to herself or her child. Yvonne...
Stamler v. Willis
In the 1960s, particularly after HUAC produced Operation Abolition, a film meant to justify the committee's existence which inadvertently underscored its high-handed tactics, people increasingly...
(-) Remove Criminalizing Dissent filter Criminalizing Dissent
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text:
Temuera Morrison's the Only Face for Boba Fetta
Alexander Aitken
Air NZ – Inspiring Voices: Dame Suzie Moncrieff
NZEDGE > News > Arts > Neill the ruthless
Neill the ruthless
Actor Sam Neill stars in the made-for-television Canada-China co-production of Iron Road as ruthless Canadian railroad baron Alfred Nichol. The historical mini-series purports to tell the story of the thousands of Chinese labourers who built the trans-Canada railway in the late 1800s. Nichol's ambition knows no bounds, imagining the coolies he's hauling in from China by the shipload — one Chinese worker is said to have died for every mile of track — are so many replaceable cogs in his unstoppable machine. "It's a part of Canadian history I knew nothing about till I saw the script," Neill said. "The other day I walked by that rather magnificent memorial to Chinese railroad workers by Eldon Garnet and Francis LeBouthillier, and I was impressed to learn how large a story it is." Work seems to keep coming Neill's way, said the one-time documentary maker. "There are no guarantees in this business, and there's nothing worse for an actor than being out of work. I like to keep busy." He's also starring — along with Ethan Hawke and Willem Dafoe — in the sci-fi vampire flick-with-a-twist, The Daybreakers, as part of September's Midnight Madness series at the Toronto International Film Festival.
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When a popular product that's been proven over many years reaches its fourth generation, there's a lot to say about it. For one, we've made the Avantgarde considerably lighter. The weight of the options has been optimised and the models further developed without giving up proven features.
In addition to its low weight, the Avantgarde DS stands out for its extremely small folding size. At the same time, it offers active wheelchair users numerous options. With its compact design and integrated leg supports, the Avantgarde DS has the lowest net weight in the Avantgarde series.


Fathima Institute of Medical Sciences & Hospital, Kadapa was established in 2010 and run by a Society. The College admission is based on common medical entrance test and other factors governed by Medical Council of India (MCI), State and Central Governments.
Candidate should have passed Intermediate or Equivalent in Biology,Physics and Chemistry Streams. Candidates who have registered for the Intermediate Second year exams for the respective year can also write the exam, but their candidature for the exam is valid only if the he/she successfully clears the Intermediate Exams that year. Candidates should be AP Residents as per the Admission Regulations defined in the A.P.Educational Institutions. Candidates should not by above 22years of age as on the date mention in that respective year.


Samsung officially announced a new 2-in-1 tablet in the market called as "Galaxy TabPro S Gold Edition." It is an upgraded variant of the Galaxy TabPro S that was first unveiled at the CES 2016. The latest Windows 10 is optimized to use with touch interface along with keyboard and mouse. By using the bundled keyboard cover, the user can also use it as a laptop, but the major disappointment is that there will be no USB or HDMI ports on this 2-in-1 tablet. Samsung is offering "multiport accessory" that brings the additional connectivity options which are missing on the tablet. This new Gold color variant comes with 8GB of RAM and 256GB of SSD storage instead of 4GB RAM and 128GB SSD storage as seen on the earlier launched variant of Galaxy TabPro S.
It will be available starting from October 14th in the U.S with a price tag of $1000. The earlier launched Galaxy TabPro S with 4GB RAM is now retailing at $800 instead of the launch price of $900. The stylus which Samsung calls the "Galaxy TabPro Pen" should be purchased separately for $80. It sports a 12-inch Full HD+ (2160 x 1440 pixels) resolution Super AMOLED display. It is powered by the 6th-gen Intel Core M3 Processor clocked at 2.2GHz. The tablet runs on the Windows 10 Home Edition and is backed by a whopping 5,200mAh battery that is mentioned to give 10.5 hours of video playback. This huge battery can be fully charged in 2.5 hours using the Samsung adaptive charging technology and USB 3.1 Type-C port.
On the camera front, there is a 5MP autofocus rear camera while the front is a 5MP fixed focus camera. More than capturing images, the cameras on this device can be used for video conferencing or Skype calls. There is no SIM card slot on this device but comes with Wi-Fi 802.11 a/b/g/n/ac and Bluetooth 4.1. This announcement comes just after the production of the Galaxy Note 7 was halted. The Galaxy Note 7 users in the U.S will be offered $100 while purchasing the Galaxy S7 or S7 Edge.While in India, where the Galaxy Note 7 hasn't yet launched, Samsung is offering several benefits if they still stick with Samsung Galaxy smartphones.


text:
Now the survivor for the assault is sharing her tale for ab muscles first time.
首页 / Mexican Ladies Online / Now the survivor for the assault is sharing her tale for ab muscles first time.
Her grandmother lives in another of the Native United states reservations down into the Lower 48, as Alaskans want to phone the mainland states, along side plenty of her cousins. "They would ask if we lived in an igloo," she said of this individuals she came across down south, "or if I rode dog sleds to college."
Drawn back again to Alaska's big town as a grown-up, Lauren made a property for by herself yet again in Anchorage, where she nevertheless has family members.
It had been a trip to her uncle that brought her towards the Spenard neighbor hood on Aug. 8, 2017, but because it ended up, he wasn't house, so she wandered up to a nearby gasoline place. She ended up being cursing her fortune, having simply missed the bus right straight back across town, each time a white toyota suv pulled up.
"He says, 'Hey, what's your title once again?'" Lauren recalled. "And we stated, 'Do we understand one another?' And then he claims, 'I'm Dan.'"
The man was high — over 6 foot 2 ins, she believed — and had a brief, scruffy beard in identical reddish color as their locks. He was using a long-sleeved red top with the sleeves rolled up. Their top ended up being nicely tucked into their jeans that are blue. He seemed smart, like he had been maneuvering to work.
She couldn't keep in mind him or not, but he was offering her a lift if she knew. She was reluctant to start with, but he seemed friendly and she had a need to get across city. Plus, she didn't desire to appear ungrateful. "Against my better judgment," she said, "I got in."
Rick Allen, who had been Anchorage region lawyer during the time of Lauren's situation, stated that in Alaska, where distances are long and conditions could be harsh, picking right on up strangers isn't any big deal: "If somebody approaches you and states, 'Hey, are you able to just simply take me personally 2 kilometers in the future?' and you're going in that way, you simply do that material."
The person asked Lauren so he could pick something up from his other car if they could make a brief stop. She consented, in which he pulled onto a quick, unpaved part road in a peaceful residential area, where high woods and leafy scrub supplied a lot of address.
He asked Lauren to leave as he loaded the SUV. "once I reach the back of the automobile, he tackles me right down to the bottom, and I also keep in mind simply getting therefore frightened," she recalled through rips. "He just completely blindsided me."
She was told by the man he'd kill her if she screamed. She promised never to. "Then he discusses me personally within my eyes and then he claims, 'Let me destroy you anyways,'" she recalled, rips streaming down her cheeks. "And he then begins choking me personally."
She'd lost her flip-flops in the struggle when she regained consciousness, Lauren realized. Barefoot and extremely shaken, she relocated to your region of the course, unexpectedly stressed he had been likely to run her over.
But amid the terror, she exhibited composure that is remarkable. As he provided her the fabric to wipe just what authorities later called "a huge splotch of ejaculate," she had been careful not to ever wipe it all away, generally there will be some kept for authorities to check. She additionally remembered to inquire about on her bag, which had her cellphone inside. Then, as Schneider drove away, "I remember thinking to myself, Get his permit dish, get their permit dish." The moment their vehicle rounded the fold, she reached into her bag, called 911, and blurted out of the plate quantity.
During the medical center, a detective revealed Lauren six pictures of various males. She had no difficulty picking him away.
"I remember those eyes…those eyes," she said. "You don't your investment face of somebody whom you thought would definitely destroy you."
Feamales in Alaska have been in more risk of being murdered by a guy than ladies in any kind of state www.hotbrides.org/mexican-brides/. A 2016 research because of the Violence Policy Center discovered the price had been almost 3 times the nationwide average. And one-third of Alaskan adult females have seen violence that is sexual in accordance with a 2015 study from the University of Alaska Anchorage Justice Center.
The statistics are worse for native ladies like Lauren. Murder could be the 3rd leading reason for death among Alaska indigenous women, in accordance with Alaska Sen. Lisa Murkowski. On some reservations, women can be 10 times prone to be killed compared to other counties. Nearly 1 / 2 of them have actually endured rape, assault, or stalking, the government present in 2012. One out of three indigenous ladies will be raped inside their life time.
The issue is perhaps not restricted to reservations or Alaska Native villages. The Urban Indian wellness Institute, a unit for the Seattle Indian wellness Board, has found documents of 31 women that are indigenous girls that has gone missing or had been murdered in Anchorage between 1975 and 2018. Only Seattle and Albuquerque, two towns and cities with roughly twice the populace of Anchorage, had more situations.
"In regards to intimate attack and violence against ladies, unfortunately that's a issue all over Alaska," stated Allen, the previous Anchorage region lawyer. "That's a challenge in rural Alaska, it is an issue in metropolitan Alaska, also it's simply something which we all have been ashamed of and would like to make an effort to improve."
Janel Gagnon, a volunteer with forget about Mat-Su, a violence that is anti–domestic running when you look at the Matanuska-Susitna Valley outside of Anchorage, relocated to hawaii 3 years ago from Portland, Oregon, but was created in Ca. Before going north, she had three big worries: winter, bears, and moose. "I've come to love the cold, I've never ever seen a bear, and I've just seen a small number of moose," she said. "But do you realize exactly what I'm afraid of now? I'm actually scared of the individuals.
"Those data mean you've got plenty of perpetrators perambulating, as well as should be perpetrators all of us know," she stated. "Why aren't we dealing with them? Because then we'd have actually to share individuals that live next door."
Ted Stevens Anchorage Airport Terminal.
After their attack on Lauren, Justin Schneider drove himself to their work during the Ted Stevens Anchorage airport terminal, among the busiest cargo airports on the planet, where he worked being an atmosphere traffic controller. As he completed later on that evening, he drove the half an hour house to Eagle River to be together with spouse and two young ones.
He had been arrested the following day.
Lauren felt relief when the news was heard by her. Section of her had feared he would somehow find her and "finish off the task."
But she had been specially surprised to understand what her attacker did for a full time income. "My first thought was this guy's more or less responsible for individuals floating around — this psychopath," she said. "Obviously there's one thing inside the mind that gets down regarding the work of killing, and it also simply blew my brain which he was at fee of all those everyday everyday lives floating around. It had been simply insane."
Simply per week after her assault, Lauren testified right in front of the jury that is grand. Schneider had been indicted on three felony fees: kidnapping, along side attack within the 2nd and degree that is third. The kidnapping cost alone carried a phrase as much as 99 years in jail.
But he additionally encountered a misdemeanor fee for what's known as first-degree harassment. This, it proved, ended up being the charge that is only experienced they are able to bring against him for masturbating and ejaculating on Lauren's face.
Under Alaska legislation, you were responsible of first-degree harassment when they subject another to "offensive real contact . with human or animal bloodstream, mucus, saliva, semen, urine, vomitus, or feces." As written, the statutory legislation covers the work to be struck with ejaculate, yet not to be masturbated on. (The statute, like numerous comparable guidelines across the united states, is primarily made to protect jail guards from inmates hurling glasses of fluids at them from their cells. Many of these statutes clearly restrict the range of victims to police officers and crisis responders.) Basically, then, Alaska's law regarded exactly just exactly what Schneider did as equal to spitting in someone's face.
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Gastro Obscura
Brouwerij't IJ
This bird-loving brewery is situated in an old municipal bathhouse, nestled beside a 300-year-old windmill.
Matthew Black (CC BY-SA 2.0)
Börkur Sigurbjörnsson (CC BY 2.0)
jamesbhess (Atlas Obscura User)
walknboston (CC BY 2.0)
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My visit in 2016 notoriousFIG (Atlas Obscura User)
Top Places in Amsterdam
The Torture Museum
Electric Ladyland: The Museum of Fluorescent Art
Our Lord in the Attic
The Brouwerij't IJ is a charming Dutch brewery situated in an old municipal bathhouse, adjacent to the nearly 300-year-old De Gooyer windmill, just on the eastern outskirts of Amsterdam's city center. Founded in 1985, it has grown into a popular and idyllic meeting spot for visitors and locals alike.
At a time when craft breweries were hard to come by in the Netherlands, founder Kasper Peterson was inspired by his experience with Belgian beer styles and, as his brewery has grown, so has its offerings and experimental nature. The ostrich-and-egg logo was also Peterson's brainchild, as he had a particular fondness for the oversized avian species (which is fitting in respect to the brewery's proximity to Amsterdam's Royal Artis Zoo).
The brewery's offerings include Belgian styles such as dubbels and tripels as well as a pilsner and IPAs. As if enjoying a beer beside a windmill wasn't enough to entice customers, the Brouwerij't IJ also serves up puns on the sly. For most unsuspecting and uninitiated tourists, it's easy for the wordplay to go right over your head since it delightfully deals with the letters i and j. In Dutch, IJ is the name of the river that the brewery sits on. Pronounced "eye," this could also be used for the Dutch word for "egg," which is actually spelled ei. Some beers on tap include the IJ Wit (or "Egg White"), the Paas IJ ("Easter Egg"), the IJndejaars ("One Year Old"), and the IJbok ("Egg Buck," whatever that is), in addition to more standard and less playfully named brews.
Continuing with its theme of avian appreciation, the brewery adopted one of the ostriches at the Artis zoo and named her Esasa, Zulu for "be happy."
There is another bar situated just before you get to the Brouwerij't IJ, profiting from the brewery's popularity and unsuspecting tourists. Don't be fooled: Keep walking through until you get to the brewery.
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Today, [McCain is] a simple opportunist who can't even be bothered to listen to nor tolerate the presence of young immigrants in his office.
Hispanics do not have a Dr. King to follow. The Hispanic community in the United States [...] has only President Obama to be their last hope in the recognition of the rights of a huge mass of illegal workers, and above all, to go against the counterrevolution driven by the extreme right, which turns anyone with Latino ethnic attributes into suspected criminals.


Online jobs, as defined in this article, are jobs that offer you the ability to work from home using your computer and in some cases, your computer and telephone. Employers pay you to perform work that you complete over the Internet.
Half of businesses will have online teams by 2020. Both a recent survey from Elance competitor oDesk and recent comments made to GigaOM by Gene Zaino, CEO of MBO Partners, have indicated that businesses increasingly see hiring contractors as a long-term strategy and competitive advantage, rather than a short-term stopgap or simple cost-cutting measure. Elance apparently agrees with Rosati explaining how more and more businesses will come to see the benefits of online hiring and come to view the practice as a normal, if not essential, business practice.
Online advertised vacancies were up 155,900 to 5,060,100 in June, according to The Conference Board Help Wanted OnLine® (HWOL) Data Series. The May Supply/Demand rate stands at 2 unemployed for each vacancy, with a total of 4.9 million more unemployed workers than the number of advertised vacancies. The number of unemployed was 9.8 million in May.
Online advertising, also called Internet marketing or Internet advertising, is a form of marketing and advertising which uses the Internet to deliver promotional marketing messages to consumers. It includes email marketing, search engine marketing (SEM), social media marketing, many types of display advertising (including web banner advertising), and mobile advertising.
Like other advertising media, online advertising frequently involves both a publisher, who integrates advertisements into its online content, and an advertiser, who provides the advertisements to be displayed on the publisher's content. Other potential participants include advertising agencies who help generate and place the ad copy, an ad server who technologically delivers the ad and tracks statistics, and advertising affiliates who do independent promotional work for the advertiser.
Online advertising is a large business and is growing rapidly. In 2011, Internet advertising revenues in the United States surpassed those of cable television and nearly exceeded those of broadcast television. In 2012, Internet advertising revenues in the United States totaled $36.57 billion, a 15.2% increase over the $31.74 billion in revenues in 2011. U.S. internet ad revenue hit a historic high of $20.1 billion for the first half of 2013, up 18% over the same period in 2012. Online advertising is widely used across virtually all industry sectors.
This article has defined online jobs as well as painted a picture of the future for online employment.
Using the right resources, you can earn a part-time or a full-time income working from the comfort of your home.


text:
Share this Story: Japan to import less oil from Middle East as demand peaks
Japan to import less oil from Middle East as demand peaks
Japanese oil refiners will cut their capacity to the lowest in four decades next year to meet a government deadline, slashing the country's Middle East imports and tightening regional fuel supplies
Haruyoshi Yamaguchi/Bloomberg News
Japanese oil refiners will cut their capacity to the lowest in four decades next year to meet a government deadline, slashing the country's Middle East imports and tightening regional fuel supplies.
Imports of crude by the world's No. 3 oil consumer could fall by up to 320,000 barrels per day (bpd) — down nearly 9 percent on last year — with Saudi Arabia, the United Arab Emirates, Kuwait and Qatar bearing the brunt of the cuts.
The contraction in one of the world's biggest oil markets adds to falling demand from the United States as shale oil output booms, and from the ailing European economy. As import demand elsewhere falls, top oil exporters are competing more intensely for the biggest growth market — China.
Japan to import less oil from Middle East as demand peaks Back to video
The combination of a declining, ageing population and improved efficiency have cut deeply into Japan's fuel consumption. The decline in 2014 demand is almost as much as the 380,000 bpd by which China's appetite for oil is expected to grow next year.
By March 2014, Japan's total refining capacity will fall to its lowest level since 1970 or just below 4 million bpd, dropping about 1 million bpd — or 20 percent — from 2010, when Tokyo issued a mandate to slim down the bloated sector with falling domestic demand.
Japan's refiners will benefit by increasing throughput at remaining facilities, but less spare capacity could lead to a growing dependence on imports of oil products such as kerosene and gas oil to meet peak seasonal demand.
Japan has already cut about 700,000 bpd of refining capacity since 2010, Thomson Reuters data shows. Still to come, two major producers are due to close one refinery each by next March.
JX Holdings will shut the 180,000-bpd crude distillation unit (CDU) at Muroran in Hokkaido, while Idemitsu Kosan Co is scrapping its oldest 120,000-bpd unit in Tokuyama, Yamaguchi Prefecture.
EFFICIENCY BOOST
The cuts follow a 2010 directive from Japan's Ministry of Economy, Trade and Industry (METI) aimed at boosting the efficiency of Japan's refiners, many of which were operating below capacity in an overcrowded market.
The directive mandated an increase in the ratio of residue cracking units to CDUs by the end of March 2014. This would allow refiners to use cheaper, heavier oils, which they could process further and export. Alternatively, refiners could meet the target by closing old, inefficient facilities.
Most refiners chose to shut inefficient units rather than invest in upgrades.
"The refiners as a group have found new cracking units difficult to justify due to falling market demand," said independent oil analyst John Vautrain, pointing to a declining population and higher fuel efficiency.
Refiners instead are targeting higher crude throughputs to boost returns, with JX and Idemitsu, for example, aiming for 90 percent to 95 percent of capacity utilisation, company sources said.
"That's the name of the game. Reducing surplus capacity will allow local refineries to maintain higher throughput," a Tokyo-based trader said. "It's looking more positive than two to three years ago when the Japanese refining sector was looking like doomsday."
The shutdowns mean Japan could cut crude imports by close to 320,000 bpd next year if JX and Idemitsu maintain current refinery utilisation rates at 80 percent, Reuters calculations show. If the two refiners raise run rates to 90 percent, imports would fall by about 140,000 bpd.
Most of the cuts will come from Saudi Arabia, the United Arab Emirates, Kuwait and Qatar, who provide the high sulphur crude used by the refineries to be shut down, although this could be offset in the near-term by lower supply from sanctions-hit Iran.
Japan's crude diet is also likely to shift to lighter grades such as Abu Dhabi's Murban which produce more valuable middle distillates and less fuel oil, traders and analysts said. Fuel oil demand is expected to fall in Japan when more nuclear reactors restart and as the power sector uses more coal and natural gas.
RAISING RUN RATES
How much refiners will be able to increase crude runs will depend on factors such as the strength of domestic oil demand, whether or not it will be cheaper to import oil products than to produce, and if Japanese oil exports can be competitive.
Japan's refineries have been traditionally higher-cost than peers in South Korea and Singapore given greater labour and operating costs, while some producers are not equipped to load large product cargoes for export.
The latest closures may not improve the competitiveness of Japan's industry as it has chosen not to pay for upgraded facilities to use cheaper crude, said Vautain.
"Reducing fixed costs would make the refiners more profitable, but has less impact on the incremental refining costs that govern international competitiveness," he said.
Domestic demand is expected to be weak, but exporters could get a boost from the weaker yen.
Oil product demand in Japan is expected to fall 1.8 percent a year on average over the next five years through 2017/18, according to government estimates.
But as Japan's spare refining capacity shrinks, the supply of oil products could tighten during peak maintenance and demand seasons, leading to more imports.
This could provide opportunities for South Korean and Singaporean refineries to export oil products to Japan.
© Thomson Reuters 2013