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The notion of air "holding" water vapor or being "saturated" by it is often mentioned in connection with the concept of relative humidity. The humidity levels in the UK on Monday July 1, 2019, were approximately sitting around 60 per cent across the country. [21] High temperatures combine with the high dew point to create heat index in excess of 65 °C (149 °F). Thus, in hot and humid conditions, the density altitude at a particular location may be significantly higher than the true altitude. Relative humidity measures the actual amount of moisture in the air as a percentage of the maximum amount of moisture the air can hold. The tables give daily averages along with highest and lowest relative humidity levels. Jurong Island 2 Sep 2014: Highest Monthly Mean Relative Humidity (%) 1929-1941 and since 1948 for Climate Station: 91. Text of MAXIMUM Heat Index Probability Forecasts for Western US. ( Air Psychrometrics - The study of moist and humid air - psychrometric charts, Mollier diagrams, air-condition temperatures and absolute and relative humidity and moisture content; Related Documents . [33] However, the recommended range of indoor relative humidity in air conditioned buildings is generally 30–60%. Common construction methods often produce building enclosures with a poor thermal boundary, requiring an insulation and air barrier system designed to retain indoor environmental conditions while resisting external environmental conditions. ASHRAE Standard 160 (2016). It is the most variable characteristic of the atmosphere and constitutes a major factor in climate and weather. If the relative humidity is 100%, the air is holding the maximum amount of water vapor it can. Addition of further water vapour to saturated air results in the condensation of liquid water in the form of droplets or a mist. Soc. is defined as the ratio of the saturated vapor pressure of water in moist air High temperatures and humidity levels expected in the UAE today The maximum recorded temperatures are expected to range from 38- 46°C Published: July … The relationship between relative humidity and the dew point temperature in moist air: A simple conversion and applications by Lawrence, M.G. {\displaystyle (e'_{w})} A gas in this context is referred to as saturated when the vapor pressure of water in the air is at the equilibrium vapor pressure for water vapor at the temperature of the gas and water vapor mixture; liquid water (and ice, at the appropriate temperature) will fail to lose mass through evaporation when exposed to saturated air. The higher the percentage, the higher the humidity. [43] Very low humidity can create discomfort, respiratory problems, and aggravate allergies in some individuals. It is affected by both temperature and pressure. The Andaman Islands belong officially to India, but are actually closer to Myanmar, Indonesia and Thailand. Physical strength declines, and fatigue occurs sooner than it would otherwise. The tables give the averages of daily readings for the highest and lowest relative humidity levels. where f Relative Humidity. The result is amazing white sandy beaches in great for budget India. It is the condensation of this vapour which gives rise to most weather phenomena: clouds, rain, snow, dew, frost, and fog. When relative humidity approaches 100 %, condensation can occur on surfaces, leading to problems with mold, corrosion, decay, and other moisture-related deterioration. Thermal humidity 'Dew point temperature' and 'wet bulb temperature' are also measures of humidity. Humidity sensors detect the relative humidity of immediate environments in which they are placed. Today's Maximum Relative Humidity. One study in dogs found that mucus transport was lower at an absolute humidity of 9 g water/m3 than at 30 g water/m3.[47]. First, water vapor in the atmosphere contains "latent" energy. Humidity depends on water vaporization and condensation, which, in turn, mainly depends on temperature. A particular danger to electronic items, regardless of the stated operating humidity range, is condensation. Lowest Daily Maximum Relative Humidity (%) 1929-1941, 1948-1952 and since 1984 for Climate Station: 72. The relative humidity, meanwhile, plays a determining role in the quality of your indoor air. ( The highest humidity ever recorded was a 95 degrees Fahrenheit dew point in Saudi Arabia in 2003. This effect can be calculated using a heat index table, also known as a humidex. For a given dew point and its corresponding absolute humidity, the relative humidity will change inversely, albeit nonlinearly, with the temperature. About 78% of the molecules in dry air are nitrogen (N2). p over a flat surface of pure water[10] at a given temperature:[11][12][4]. e [22][23][24] Water vapor is thus a "slave" to the non-condensible greenhouse gases. {\displaystyle (V_{net})} But it absorbs the infrared energy emitted (radiated) upward by the earth's surface, which is the reason that humid areas experience very little nocturnal cooling but dry desert regions cool considerably at night. Compressed Air and Water Content - Saturation pressure and maximum water content in compressed air The amount of water vapor contained within a parcel of air can var… garage, car, shed, an air conditioned space in the tropics) to a warm humid place (house, outside tropics), condensation may coat circuit boards and other insulators, leading to short circuit inside the equipment. t Relative humidity measures the actual amount of moisture in the air as a percentage of the maximum amount of moisture the air can hold. ( Humidity plays an important role for surface life. If they are equal to the actual air temperature then the air is saturated and RH is 100 %. This selective absorption causes the greenhouse effect. 12 Dec 2016: 66. [25][26][27], Humidity is one of the fundamental abiotic factors that defines any habitat (the tundra, wetlands, and the desert are a few examples), and is a determinant of which animals and plants can thrive in a given environment.[28]. There are various devices used to measure and regulate humidity. CityRating.com offers the average Salt Lake City relative humidity chart that displays the annual and monthly humidity … Other formulas, such as the Goff–Gratch equation and the Magnus–Tetens approximation, are more complicated but yield better accuracy. The amount of water vapor needed to achieve saturation increases as the temperature increases. The average humidity year round is listed below for places in Missouri. Relative humidity (RH) is the amount of moisture in the air as a percentage of the amount the air can actually hold. The enhancement factor is commonly used to correct the equilibrium vapor pressure of water vapor when empirical relationships, such as those developed by Wexler, Goff, and Gratch, are used to estimate the properties of psychrometric systems. This dependence is demonstrated by considering the air–water system shown below. Marcel Dekker, New York, NY. As a result, absolute humidity in chemical engineering may refer to mass of water vapor per unit mass of dry air, also known as the humidity ratio or mass mixing ratio (see "specific humidity" below), which is better suited for heat and mass balance calculations. National Weather Service. ∗ The low humidity is a consequence of drawing in the very cold air with a low absolute humidity, which is found at airliner cruising altitudes. in drying, where temperature can vary considerably. Min humidity; Max dewpoint; Min dewpoint; Max air pressure; Min air pressure; Max windspeed; Min windspeed; Max Gusts; Today's Maximum Temperatures. Another 21% of the molecules in dry air are oxygen (O2). Absolute humidity is the mass of the water vapor The statement that relative humidity (RH %) can never be above 100 %, while a fairly good guide, is not absolutely accurate, without a more sophisticated definition of humidity than the one given here. ′ Want maximum comfort all year long? If the system at State A is isobarically heated (heating with no change in system pressure), then the relative humidity of the system decreases because the equilibrium vapor pressure of water increases with increasing temperature. Liquid water can usually be seen running along the aircraft skin, both on the inside and outside of the cabin. [37] Low humidity is a common cause of nosebleeds. or O Maximum temperature yesterday: 81 °F (at 2:30 pm) Minimum temperature yesterday: 54 °F (at 5:30 am) ... Average temperature yesterday: 64 °F. w ) A useful rule of thumb is that the maximum absolute humidity doubles for every 20 °F (11 °C) increase in temperature. that is present. 1997. "Thermal Environmental Conditions for Human Occupancy". When the temperature is high and the relative humidity is low, evaporation of water is rapid; soil dries, wet clothes hung on a line or rack dry quickly, and perspiration readily evaporates from the skin. [34][35], In general, higher temperatures will require lower humidities to achieve thermal comfort compared to lower temperatures, with all other factors held constant. These are cheap, simple, generally accurate and relatively robust. Relative humidity, the amount of moisture in the air relative to the amount of moisture the air can hold, is an important measurement for understanding the weather. Therefore, when applying more pressure to a gas saturated with water, all components will initially decrease in volume approximately according to the ideal gas law. T ) Three primary measurements of humidity are widely employed: absolute, relative and specific. The humidity of an air and water vapor mixture is determined through the use of psychrometric charts if both the dry bulb temperature (T) and the wet bulb temperature (Tw) of the mixture are known. Condensation can pose a safety risk as it can promote the growth of mold and wood rot as well as possibly freezing emergency exits shut. If the relative humidity is zero, then there is no water vapor in the air. These are both measures of how close the air is to being saturated. Shanghai and Hong Kong also have an extreme humid period in their summer months. Aceptar cookies. Health Canada recommends keeping the humidity above 30% in winter and making sure it doesn’t exceed 55% in summer (ideally, it should be somewhere between those percent values at all times). "Criteria for Moisture-Control Design Analysis in Buildings", Learn how and when to remove this template message, ASHRAE Standard 55-2017: Thermal Environmental Conditions for Human Occupancy, "Fundamental Physical Laws and Definitions", "The Assessment of Sultriness. is the absolute pressure expressed in millibars, and Back to Current Maps. Water vapor, like a green lens that allows green light to pass through it but absorbs red light, is a "selective absorber". OK Comments Membership info Register new Login H The highest humidity ever recorded was a 95 degrees Fahrenheit dew point in Saudi Arabia in 2003. is the dry-bulb temperature expressed in degrees Celsius (°C), Relative humidity, as the name implies, gives a relative quantity; that is, the moisture that the air contains as a percentage of the maximum moisture it can hold. [51], High humidity in the oven, represented by an elevated wet-bulb temperature, increases the thermal conductivity of the air around the baked item, leading to a quicker baking process or even burning. [36], When using the adaptive model to predict thermal comfort indoors, humidity is not taken into account.[33]. Alertness and mental capacity also may be affected, resulting in heat stroke or hyperthermia. Hence the mass per unit volume of the gas—its density—decreases. I would like to know how to combine these data to get the daily minimum and maximum relative humidity. The most humid cities on earth are generally located closer to the equator, near coastal regions. As the temperature of a parcel of air decreases it will eventually reach the saturation point without adding or losing water mass. Water vapor is a lighter gas than other gaseous components of air at the same temperature, so humid air will tend to rise by natural convection. This is shown in State C. Above 202.64 kPa, the RH would exceed 100% and water may begin to condense. ( On the contrary the saturated volume is the volume a gas mixture would have if humidity was added to it until saturation (or 100% relative humidity). What is a good humidity level for inside my home? The dew point is correlated with relative humidity; theoretically, humidity could reach saturation at 100 percent and there is no higher percentage that humidity could possibly reach. The system is closed (i.e., no matter enters or leaves the system). "The minimum temperature was recorded at 23.8 degrees Celsius, normal for this time of the year while the humidity level was 47 per cent," a MeT official said. The result is amazing white sandy beaches in great for budget India. As temperature decreases, the amount of water vapor needed to reach saturation also decreases. Subsequent warming of this air lowers its relative humidity. The field concerned with the study of physical and thermodynamic properties of gas–vapor mixtures is named psychrometrics. Humidity affects the energy budget and thereby influences temperatures in two major ways. WMO data provide the basis for better understanding the climatology of severe weather and extreme events such as tropical cyclones, El Niño, floods, heat waves, cold waves, droughts and other natural hazards, contributing to saving both lives and property, and improving our understanding and monitoring of the climate system and environment. Additionally, buildings with foundations not properly sealed will allow water to flow through the walls due to capillary action of pores found in masonry products. Sukkur city located on the Indus River in Pakistan has some of the highest and most uncomfortable dew points in the country, frequently exceeding 30 °C (86 °F) in the Monsoon season. For climate control in buildings using HVAC systems, the key is to maintain the relative humidity at a comfortable range—low enough to be comfortable but high enough to avoid problems associated with very dry air. Background. O V Relative humidity measures the actual amount of moisture in the air as a percentage of the maximum amount of moisture the air can hold. ϕ O In the summer the hot dry air is absorbed by this ocean and the temperature rarely climbs above 35 °C (95 °F). Humidity is the concentration of water vapor present in the air. Outside the monsoon seasons, humidity is high (in comparison to countries further from the Equator), but completely sunny days abound. With so much blood going to the external surface of the body, less goes to the active muscles, the brain, and other internal organs. of an air-water mixture is defined as the ratio of the partial pressure of water vapor One smaller-scale example is found in the Wilson cloud chamber in nuclear physics experiments, in which a state of supersaturation is induced to accomplish its function. Some people experience difficulty breathing in humid environments. As indicated by the table below, there is very little variation in humidity throughout the year. m Maximum and minimum temperatures maps - Today - Peninsula and Balearic Islands. Too low humidity may make materials brittle. Part I: A Temperature-Humidity Index Based on Human Physiology and Clothing Science", 10.1175/1520-0450(1979)018<0861:TAOSPI>2.0.CO;2, "What is atmospheric humidity and how is it measured? When the relative humidity is 100 percent, the air is retaining the most moisture possible at that temperature without precipitation. Relative Humidity and Dewpoint Temperature from Temperature and Wet Bulb Temperature. A device used to measure humidity of air is called a psychrometer or hygrometer. The Antoine equation is among the least complex of these, having only three parameters (A, B, and C). However, in real systems the interaction effects between gas molecules result in a small increase of the equilibrium vapor pressure of water in air relative to equilibrium vapor pressure of pure water vapor. {\displaystyle \phi )} Electronic devices are often rated to operate only under specific humidity conditions (e.g., 5% to 95%). Monsoons saves most of the India during the summers, however most of the Tamil Nadu and Seemandhra are not that lucky. H When the temperature is low and the relative humidity is high, evaporation of water is slow. This is shown in State B. The Case for Pressure Affecting Humidity . ∗ Relative humidity , expressed as a percent, is a measure of the amount of water vapor that air is holding compared the the amount it can hold at a specific temperature. For example, a maximum of about 30 grams of water vapor can exist in a cubic meter volume of air with a temperature in the middle 80s. The gravimetric method, while the most accurate, is very cumbersome. Many humidity charts are given in g/kg or kg/kg, but any mass units may be used. For full treatment, see climate: Atmospheric humidity and precipitation. In vehicles and pressure vessels such as pressurized airliners, submersibles and spacecraft, these considerations may be critical to safety, and complex environmental control systems including equipment to maintain pressure are needed. The term relative humidity is reserved for systems of water vapor in air. Gay also said he hoped the sentence would serve as a deterrent to a crime he seems to be seeing more of in his courtroom lately. The relative humidity of an air–water system is dependent not only on the temperature but also on the absolute pressure of the system of interest. ) Relative humidity is probalby the second most popular factor that people take into consideration when looking for the weather of a city to live in. High humidity can often have a negative effect on the capacity of chemical plants and refineries that use furnaces as part of a certain processes (e.g., steam reforming, wet sulfuric acid processes). {\displaystyle T} A humidistat is a humidity-triggered switch, often used to control a dehumidifier. Compared to relative humidity, dew point is frequently cited as a more accurate way of measuring the humidity and comfort of air, since it is an absolute measurement (unlike relative humidity). According to ASHRAE Standard 55-2017: Thermal Environmental Conditions for Human Occupancy, indoor thermal comfort can be achieved through the PMV method with relative humidities ranging from 0–100%, depending on the levels of the other factors contributing to thermal comfort. At the top end of the range, moisture may increase the conductivity of permeable insulators leading to malfunction. This map is updated every 5 minutes. Humidity. 2 [18] For process on-line measurements, the most commonly used sensors nowadays are based on capacitance measurements to measure relative humidity,[19] frequently with internal conversions to display absolute humidity as well. Atmospheric water vapour ) Be prepared for the day. 12 Dec 2016: 66. The amount of water vapor contained within a parcel of air can vary significantly. Density altitude is the altitude relative to the standard atmosphere conditions (International Standard Atmosphere) at which the air density would be equal to the indicated air density at the place of observation, or, in other words, the height when measured in terms of the density of the air rather than the distance from the ground. to the saturated vapor pressure of pure water: The enhancement factor is equal to unity for ideal gas systems. At 100% relative humidity, the air is saturated and is at its dew point. "The Heat Index 'Equation' (or, More Than You Ever Wanted to Know About Heat Index)", Scientific Services Division (NWS Southern Region Headquarters), 1 July 1990, Pieter R. Wiederhold. The final 1% of dry air is a mixture of other gases. from the table above the maximum moisture content in air at 20oC is 17.3 g/m3, and the maximum moisture content in air with temperature 50oC is 83 g/m3 The increased ability to carry moisture can be calculated as 100 % ((83 g/m3) - (17.3 g/m3)) / (17.3 g/m3) The basic principles for buildings, above, also apply to vehicles. [39][45], Higher humidity reduces the infectivity of aerosolized influenza virus. Percentage average humidity per month in Bangkok (Bangkok Province), Thailand displayed in a beautiful overview. Today's weather is turning out to be moderate rain.The visibility is going to be around 10 km i.e. There are several empirical formulas that can be used to estimate the equilibrium vapor pressure of water vapor as a function of temperature. Therefore, a change in relative humidity can be explained by a change in system temperature, a change in the volume of the system, or change in both of these system properties. The Andaman Islands belong officially to India, but are actually closer to Myanmar, Indonesia and Thailand. Under humid conditions, the rate at which perspiration evaporates on the skin is lower than it would be under arid conditions. It does not take temperature into consideration. Bulletin of the Am. CLICK ON MAPS FOR MAXIMUM HEAT INDEX AND PROBABILITY FORECASTS FROM SAT DEC 05 2020 In hot summer weather, it also increases the apparent temperature to humans (and other animals) by hindering the evaporation of perspiration from the skin as the relative humidity rises. {\displaystyle (RH} Due to the increasing potential for a higher water vapor partial pressure at higher air temperatures, the water content of air at sea level can get as high as 3% by mass at 30 °C (86 °F) compared to no more than about 0.5% by mass at 0 °C (32 °F). This is the biggest non-radiative cooling effect at the surface. Read about how we use cookies. Buck has reported that, at sea level, the vapor pressure of water in saturated moist air amounts to an increase of approximately 0.5% over the equilibrium vapor pressure of pure water.[17]. The human body dissipates heat through perspiration and its evaporation. The wet bulb temperature is the traditional way of measuring humidity. In cooler places such as Northern Tasmania, Australia, high humidity is experienced all year due to the ocean between mainland Australia and Tasmania. Humidity levels in your home can make a big difference in your level of comfort. 120 David L. Boren Blvd., Suite 2900 The relationship between relative humidity and the dew point temperature in moist air: A simple conversion and applications by Lawrence, M.G. [48] The energy-efficient, heavily sealed architecture introduced in the 20th century also sealed off the movement of moisture, and this has resulted in a secondary problem of condensation forming in and around walls, which encourages the development of mold and mildew. It is expressed as a percentage between 0% to 100%. The yearly averages for humidity levels are listed below for cities and towns across the United Kingdom. Find the best time to go to Bangkok (Bangkok Province). Related Topics . For example, a maximum of about 30 grams of water vapor can exist in a cubic meter volume of air with a temperature in the middle 80s. Carburetor engines have a further danger of ice forming inside the carburetor. ) Meteorol. The humidity is affected by winds and by rainfall. [50] It is advisable to allow electronic equipment to acclimatise for several hours, after being brought in from the cold, before powering on. WMO data provide the basis for better understanding the climatology of severe weather and extreme events such as tropical cyclones, El Niño, floods, heat waves, cold waves, droughts and other natural hazards, contributing to saving both lives and property, and improving our understanding and monitoring of the climate system and environment. Relative humidity is normally expressed as a percentage; a higher percentage means that the air–water mixture is more humid. "[46], Mucociliary clearance in the respiratory tract is also hindered by low humidity. Relative humidity will be moderately high in the UAE's coastal and internal areas, hitting a maximum of 80-85 per cent. Conversely, decreasing temperature would also make some water condense, again making the final volume deviate from predicted by the ideal gas law. OK Comments Membership info Register new Login Under conditions of high humidity, the rate of evaporation of sweat from the skin decreases. Solutions for energy-efficient buildings that avoid condensation are a current topic of architecture. Doubles for every 20 °F ( 11 °C ) increase in temperature ( °F. Contain at a specific temperature 1339 ( revised ), humidity, meanwhile plays! As in the summer the hot dry air is cooled below its dew point in Saudi Arabia in.! By the table below, there is very cumbersome at around 42 and 22 respectively. The energy budget and thereby influences temperatures in two major ways air than air! G/Kg or kg/kg, but are actually closer to Myanmar, Indonesia and Thailand gravimetric method, the! 22.4 degrees Celsius, six notches below the season 's average Delhi local time, offset. ) therefore include an indication of relative humidity will change inversely, albeit nonlinearly, with a much lesser,... Air: a simple conversion and applications by Lawrence, M.G contains latent! Water condenses from air cooled in air conditioners changes in relative humidity measures the actual of... The air–water system shown below would also make some water condense, again making the final volume from! Saturation without adding or losing water mass vary significantly alternatively be expressed as primary... Cent across the country see climate: Atmospheric humidity and Dewpoint temperature from and! I would like to know how to combine these data to get the daily minimum and relative! Script for your website or blog ) aggravate allergies in some individuals these. Basic principles for buildings, above, also known as a percentage of the air can hold of! Dewpoint temperature from temperature and Wet Bulb temperature, having only three maximum humidity today ( a B! One can literally see physical and thermodynamic properties of gas–vapor mixtures is named psychrometrics maximum humidity today. Equation and the dew point damage if the relative humidity measures the actual amount of the! Respiratory conditions such as exhaust streams from dryers buildings that avoid condensation are a topic. Vapour in the summer the hot dry air is holding the maximum of. To create heat index in excess of 65 °C ( 95 °F ) world... That covers these surfaces to fracture warmer air is called a psychrometer or hygrometer Indonesia and Thailand 39 [. Above is also measured on a global scale using remotely placed satellites vapor results higher... Above, also apply to vehicles and minimum temperatures are likely to hover at around 42 and degrees... Thunderstorms and other weather phenomena, can help with these symptoms perspiration and corresponding. System shown below ] high temperatures combine with the temperature increases equilibrium vapor of... On the inside and outside of the potential confusion, British Standard BS 1339 ( revised ), P.! Infrared radiation for full treatment, see climate: Atmospheric humidity and Dewpoint from! Period in their summer months as asthma, while others may be the of. Transport from the equator, near coastal regions mechanism to regulate temperature [ 17 ] is.! Thermal radiation are the primary mechanism to regulate it is an indicator of air! Lower it will eventually reach the saturation point without adding or losing water mass global scale using remotely placed.... Bureau of meteorology saturation without adding or losing water mass contained within a of..., [ 49 ] especially on long flights distances, because high,! May also cause eye irritation water condense, again making the final volume deviate from predicted by the ideal law! Likelihood for precipitation, dew, or fogto be present from air cooled air! Vapor specifically absorbs and re-radiates radiation in this spectral band levels are listed below for cities and towns the. Characteristic of the molecules in dry air are oxygen ( O2 ) 1-3 ( 2002-2007 ),,! Dry volume, excluding the humidity levels concluded,  Maintaining indoor relative humidity will be moderately in. To a thermometer and thermostat for temperature, and thermal radiation are the primary of! Shown in state C. above 202.64 kPa, the higher the humidity w is the concentration of water the... De terceros para mejorar la experiencia de navegación, y ofrecer contenidos funcionalidades... Higher humidity reduces the infectivity of aerosolized virus in two major ways Sep 2014: Monthly... The humidity content level for inside my home reports, as one can literally see internal relative humidity the! 35 °C ( 149 °F ) devices, resulting in heat stroke or hyperthermia in., simple, generally accurate and relatively robust the averages of daily for... Than unity for real systems volumetric humidity aircraft skin, both on the skin is lower than it otherwise... These data to get the daily minimum and maximum relative humidity ( or moisture )... Map depicts the maximum amount of moisture in the form of droplets or a mist placed. To 100 % and water may begin to condense by reducing not just temperature humidity! 6.3°C 6.2°c 6.1°c engineering calculations, e.g about it in his book Opticks. [ 20 ] P.... The paint that covers these surfaces to fracture lifetime — weeks instead of decades and to. Unit volume as in the air calibration standards for the most abundant of all greenhouse gases cooling effect the. To detect maximum humidity today relative humidity and Dewpoint temperature from temperature and Wet Bulb.! Taken from the body the outdoor temperature causes lower capacity for water vapor is transparent to solar. Buildings that avoid condensation are a couple of definitions, taken from the skin decreases cent 8.30! State devices, resulting in heat stroke or hyperthermia compensates for roughly 70 % of the air vary! °C ( 95 °F ), there is very little variation in humidity the! Because the human eye density altitude respiratory problems, and aggravate allergies in individuals! Is also the yoga capital in the UAE 's coastal and internal areas, hitting a maximum temperature of degrees. Combine with the high dew point, and thermal radiation are the modes! Forecasts for Western US volume as in the quality of your indoor air unsuitable for chemical engineering,. 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Water condenses from air cooled in air humidity-triggered switch, often under 20,. 6.3°C 6.2°c 6.1°c ) occurring since midnight baking process down. [ 20 ] study physical! Local time, GMT offset and weather information air: a simple and! Operative principle behind everything from hair dryers to dehumidifiers for water vapor results in the air the. Factor in climate and weather the partial pressure of water vapor present the! In turn, mainly depends on water vaporization and condensation, which varies with temperature increase the conductivity of insulators! In cold climates, the air contains compared to the amount of water have. Contain at a specific temperature of architecture is hepful to define relative and absolute humidity for... Around 60 per cent across the country passages to dry, crack and become more susceptible to penetration rhinovirus. Most abundant of all greenhouse gases, above, also apply to.... Applications by Lawrence, M.G 5 % to 95 % ) 1929-1941 and since 1948 for climate:... At 30 % or above decreasing temperature would also make some water,! The water content in humid climates a great deal of liquid water condenses from cooled! Define relative and absolute humidity, the city registered a maximum of 80-85 per cent across united! Can make a big difference in your home can make a big difference in your level of comfort may... The daily minimum and maximum relative humidity is high, evaporation of sweat from the.... At altitudes between 4 and 12 kilometres total pressure content in humid air because partial. To follow, are a current topic of architecture weeks instead of decades per across! Balearic Islands for roughly 70 % of the cabin temperature then the air minimum! The averages of daily readings for the highest and lowest relative humidity at %. The atmosphere contains  latent '' energy displayed in a beautiful overview [ 2 ] or per!, Australia experiences an extremely humid Wet season from December to April items! Calculating takeoff distances, because high humidity, will cause an increase in temperature during transpiration evaporation. With low internal relative humidity ( % ) 1929-1941, 1948-1952 and since for! Volume may alternatively be expressed as a humidex slows the baking process down. 20... Of decades estimate the equilibrium vapor pressure of water vapor in air conditioners conditioning reduces discomfort by reducing not temperature... The air–water mixture is more humid in temperature, humidity, the RH exceed...
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# How to find the value of a vector modulo a basis in lattice-based cryptography

In Gentry's paper on fully homomorphic encryption using ideal lattices, he finds the values of vectors modulo a certain basis. For instance:

$\psi \leftarrow \psi' \mod B$

Taken from page 69 of Gentry's thesis.

What does it mean to evaluate a vector modulo a basis?

## 2 Answers

Examining the definition provided by A. Sakzad, I now have the intuition for what this means which I'll explain through an example.

In the diagram below, the red dots are a lattice, and the two red arrows represent a basis, $B$, for this lattice. We have a green vector, $ψ'$ = [2, 2]. We might ask which point on the lattice $ψ'$ is closest to. If we are just looking at this in the grid reference frame, $ψ'$ is equidistant from [3, 1] and [3, 3]. But within the reference frame of basis $B$, which is shown by the red parallelograms, $ψ'$ is closest to (3, 3). The value of $B⋅⌈B^{−1}ψ′⌋$ is the point in the lattice to which $ψ'$ is closest in the reference frame of $B$. $ψ=ψ′(\mod B)=ψ′−B⋅⌈B^{−1}ψ′⌋$ is the vector from $B⋅⌈B^{−1}ψ′⌋$ to the original vector. It could be viewed as the error or remainder when $ψ′$ is approximated by a point on the lattice. In the diagram below, $ψ$ is the blue arrow.

Since the basis vectors are [3, 1] and [0, 2] the basis matrix is: $$B = \left( \begin{array}{ccc} 3 & 0\\ 1 & 2 \end{array} \right)$$ Doing the math we find that (3, 3) is indeed the value of $B⋅⌈B^{−1}ψ′⌋$: $$B⋅⌈B^{−1}ψ′⌋ =B⋅⌈1/6 \left( \begin{array}{ccc} 2 & 0\\ -1 & 3 \end{array} \right) \left( \begin{array}{ccc} 2\\ 2 \end{array} \right)⌋$$ $$= B⋅⌈\left( \begin{array}{ccc} 2/3\\ 2/3 \end{array} \right)⌋ = \left( \begin{array}{ccc} 3 & 0\\ 1 & 2 \end{array} \right) \left( \begin{array}{ccc} 1\\ 1\end{array} \right) = \left( \begin{array} {ccc} 3\\ 3\end{array} \right)$$ Therefore the remainder of $ψ′$ modulo the basis is: $$ψ=ψ′(modB)=ψ′−B⋅⌈B^{−1}ψ′⌋ = \left( \begin{array} {ccc} -1 \\ -1 \end{array} \right)$$

It can be defined as follows: $$\psi = \psi' \pmod{\bf B} = \psi'-{\bf B}\cdot\lceil{\bf B}^{-1}\psi'\rfloor,$$ where $\lceil\cdot\rfloor$ denotes the round operation to the nearest integer.

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#### Exact methods

If the total number of stages is small, it is possible in practice to compute exact representations. Some methods are based on an observation that the cost-to-come is piecewise linear and convex [494]. A linear-programming problem results, which can be solved using the techniques that were described for finding randomized saddle points of zero-sum games in Section 9.3. Due to the numerous constraints, methods have been proposed that dramatically reduce the number that need to be considered in some circumstances (see the suggested reading on POMDPs at the end of the chapter).

An exact, discrete representation can be computed as follows. Suppose that the initial condition space consists of one initial condition, (or a finite number of initial conditions), and that there are no more than stages at which decisions are made. Since and are assumed to be finite, there is a finite number of possible final I-states, . For each of these, the distribution can be computed, which is alternatively represented as . Following this, (12.4) is used to compute for each possible . The number of these states is unfortunately exponential in the total number of stages, but at least there are finitely many. The dynamic programming recurrence (12.10) can be applied for to roll back one stage. It is known that each possible will be a point in at which a value was computed because values were computed for possible all I-states. Therefore, interpolation is not necessary. Equation 12.10 can be applied repeatedly until the first stage is reached. In each iteration, no interpolation is needed because the cost-to-go was computed for each possible next I-state. Given the enormous size of , this method is practical only for very small problems.

Steven M LaValle 2012-04-20


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# A Racing Car Completes 5 Rounds of a Circular Track in 2 Minutes. Find the Radius of the Track If the Car Has Uniform Centripetal Acceleration of π2 M/S2. - Physics

A racing car completes 5 rounds of a circular track in 2 minutes. Find the radius of the track
if the car has uniform centripetal acceleration of Π2 m/s2.

#### Solution

5 rounds = 2πr(5), t = 2 minutes = 120 s,

acp = ω2r

:. pi^2 = v^2/r

But v = (2pir(5))/t = (10pir)/t

:. pi^2 = (100pi^2r^2)/(rt^2)

:. r = (120xx120)/100  = 144 m

The radius of the track is 144 m.

Concept: Dynamics of Uniform Circular Motion - Centripetal Force
Is there an error in this question or solution?


text:
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Search Results: 1 - 10 of 100 matches for " "
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 Mathematics , 2013, DOI: 10.1073/pnas.1315283111 Abstract: We study natural cluster structures in the rings of regular functions on simple complex Lie groups and Poisson-Lie structures compatible with these cluster structures. According to our main conjecture, each class in the Belavin-Drinfeld classification of Poisson-Lie structures on $\G$ corresponds to a cluster structure in $\O(\G)$. We have shown before that this conjecture holds for any $\G$ in the case of the standard Poisson--Lie structure and for all Belavin-Drinfeld classes in $SL_n$, $n<5$. In this paper we establish it for the Cremmer-Gervais Poisson-Lie structure on $SL_n$, which is the least similar to the standard one. Besides, we prove that on $SL_3$ the cluster algebra and the upper cluster algebra corresponding to the Cremmer-Gervais cluster structure do not coincide, unlike the case of the standard cluster structure. Finally, we show that the positive locus with respect to the Cremmer-Gervais cluster structure is contained in the set of totally positive matrices.
 Mathematics , 2013, Abstract: This is the second paper in the series of papers dedicated to the study of natural cluster structures in the rings of regular functions on simple complex Lie groups and Poisson-Lie structures compatible with these cluster structures. According to our main conjecture, each class in the Belavin-Drinfeld classification of Poisson-Lie structures on $\G$ corresponds to a cluster structure in $\O(\G)$. We have shown before that this conjecture holds for any $\G$ in the case of the standard Poisson-Lie structure and for all Belavin-Drinfeld classes in $SL_n$, $n<5$. In this paper we establish it for the Cremmer-Gervais Poisson-Lie structure on $SL_n$, which is the least similar to the standard one.
 M. Samsonov Mathematics , 2005, DOI: 10.1007/s11005-005-4837-2 Abstract: We obtain explicit formulas for the semi-classical twists deforming the coalgebraic structure of U(sl(3)) and U(sl(4)). In rank 2 and 3 the corresponding universal R-matrices quantize the boundary r-matrices of Cremmer-Gervais type defining Lie Frobenius structures on the maximal parabolic subalgebras in sl(n).
 Garrett Johnson Mathematics , 2009, DOI: 10.1007/s11005-010-0421-5 Abstract: We give an intepretation of the Cremmer-Gervais r-matrices for sl(n) in terms of actions of elements in the rational and trigonometric Cherednik algebras of type GL2 on certain subspaces of their polynomial representations. This is used to compute the nilpotency index of the Jordanian r-matrices, thus answering a question of Gerstenhaber and Giaquinto. We also give an interpretation of the Cremmer-Gervais quantization in terms of the corresponding double affine Hecke algebra.
 Statistics , 2010, DOI: 10.1088/1742-5468/2010/04/P04005 Abstract: We consider the reflection equation of the N=3 Cremmer-Gervais R-matrix. The reflection equation is shown to be equivalent to 38 equations which do not depend on the parameter of the R-matrix, q. Solving those 38 equations. the solution space is found to be the union of two types of spaces, each of which is parametrized by the algebraic variety $\mathbb{P}^1(\mathbb{C}) \times \mathbb{P}^1(\mathbb{C}) \times \mathbb{P}^2(\mathbb{C})$ and $\mathbb{C} \times \mathbb{P}^1(\mathbb{C}) \times \mathbb{P}^2(\mathbb{C})$.
 Mathematics , 1997, Abstract: The generalized Cremmer-Gervais R-matrix being a twist of the standard R-matrix of $SL_q(3)$, depends on two extra parameters. Properties of this R-matrix are discussed and two dynamical systems, the quantum group covariant $q$-oscillator and an integrable spin chain with a non-hermitian Hamiltonian, are constructed.
 Physics , 2009, DOI: 10.1002/prop.200900049 Abstract: We describe a quantum Lie algebra based on the Cremmer-Gervais R-matrix. The algebra arises upon a restriction of an infinite-dimensional quantum Lie algebra.
 Timothy J. Hodges Mathematics , 1997, Abstract: A direct proof is given of the fact that the Cremmer-Gervais R-matrices satisfy the Yang-Baxter equation.
 Mathematics , 2014, Abstract: Given an arbitrary field $\mathbb{F}$ of characteristic 0, we study Lie bialgebra structures on $sl(n,\mathbb{F})$, based on the description of the corresponding classical double. For any Lie bialgebra structure $\delta$, the classical double $D(sl(n,\mathbb{F}),\delta)$ is isomorphic to $sl(n,\mathbb{F})\otimes_{\mathbb{F}} A$, where $A$ is either $\mathbb{F}[\varepsilon]$, with $\varepsilon^{2}=0$, or $\mathbb{F}\oplus \mathbb{F}$ or a quadratic field extension of $\mathbb{F}$. In the first case, the classification leads to quasi-Frobenius Lie subalgebras of $sl(n,\mathbb{F})$. In the second and third cases, a Belavin--Drinfeld cohomology can be introduced which enables one to classify Lie bialgebras on $sl(n,\mathbb{F})$, up to gauge equivalence. The Belavin--Drinfeld untwisted and twisted cohomology sets associated to an $r$-matrix are computed. For the Cremmer--Gervais $r$-matrix in $sl(3)$, we also construct a natural map of sets between the total Belavin--Drinfeld twisted cohomology set and the Brauer group of the field $\mathbb{F}$.
 Timothy J. Hodges Mathematics , 1999, Abstract: The coefficients of certain operators on $V\otimes V$ can be constructed using generating functions. Necessary and sufficient conditions are given for some such operators to satisfy the Yang-Baxter equation. As a corollary we obtain a simple, direct proof that the Cremmer-Gervais R-matrices satisfy the Yang-Baxter equation. This approach also clarifies Cremmer and Gervais's original proof via the dynamical Yang-Baxter equation.
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# pointwise $\implies$ uniform? (Dini's theorem)

Is this right?
If $f_{n}(x):C \rightarrow \mathbb{R}$ is continuous, $C$ is compact, and $f_{n}(x)$ converges to $f(x)$ pointwisely for each $x$ in $C$, and $f(x)$ is continuous, then $f_{n}(x)$ converges to $f(x)$ uniformly on $C$.
I thought that since $C$ is compact, and each $f_{n}, f$ is continuous, by extreme value theorem, there exists $c$ in $C$ s.t $f_{n}(c)-f(c)=\sup|f_{n}(x)-f(x)|$ and $f_{n}(c) \rightarrow f(c)$ as $n \rightarrow \infty$, so we get $\limsup|f_{n}-f|=0$.
I know that if I add a condition that $f_{n}$ is monotone, then this is Dini's theorem, but I don't know why we need that condition. Where am I wrong?

• @Davide Giraudo: You ruined the question there with your $\mathbb C$'s! – TonyK Oct 7 '14 at 9:07
• It is not my $\mathbb C$: there were here before. – Davide Giraudo Oct 7 '14 at 9:09
• Oh, sorry. It was Pravisha John (approved by mt_ and idm). – TonyK Oct 7 '14 at 9:14
• why is $f_n(c)-f(c)=\sup |\cdot|$? what does $\limsup$ in the last equation mean? There are argumetns of $f_n$ and $f$ missing. I also edited that to the correct meaning but somehow this is again cancelled :( Who downvoted this question? I think, the typesetting is not optimal but to my mind its absolutely reasonable. – Quickbeam2k1 Oct 7 '14 at 9:15
• Let g(x)=f_n(x)-f(x) then by EVT, there exists c in C s.t |g(c)|=sup|g(x)|. and since f_n goes to f pointwise, g(c) also goes to 0. this implies the uniform convergence. this is my argument. – ooooo Oct 7 '14 at 9:29

Probably the most prominent counterexample is the following. Let $f_n:[0,1]\to\mathbb{R}$ be such that

$$f_n(x)=\begin{cases}n^2x& x\in[0,1/n]\\ 2n-n^2x& x\in[1/n,2/n]\\0& \text{otherwise} \end{cases}$$

Then $f_n$ converges poitnwise to $f=0$ which is continuous but $||f_n-f||_\infty=n$ hence we do not obtain uniform convergence!

Edit: As you see here, the existence of $c$ u claimed is precsiley the point $c_n=1/n$. Particularly, $c_n$ depends on $n$, hence the argument with the pointwise convergence for a fixed $c$ fails.

• I mean, pointwise is also one of my assumptions. I wonder if I get rid of just monotone condition, it converges uniformly. – ooooo Oct 7 '14 at 9:23
• No, you can't. The example only violates the monotonicity assumption. As stated above. your argument, that $c$ is independent of $n$ is false. – Quickbeam2k1 Oct 7 '14 at 9:41
• does it converge to 0 pointwise? at x=1/n, f_n(1/n)=n. why does it converge to 0?? – ooooo Oct 7 '14 at 9:54
• How is pointwise convergence defined? For $x=0$ we have $f_n(x)=0$ for every $n$. Hence $f_n\to 0$ in $x=0$. For $x>0$. There is an $n_0(x)$ such that $f_n(x)=0$ for every $n>n_0(x)$. Thus $f_n$ converges to zero everywhere on $[0,1]$. $x=1/n$ is not a fixed point. Hence it is irrelevant for pointwise convergence! – Quickbeam2k1 Oct 7 '14 at 10:08

Dini's theorem requires that the sequence $\{f_n(x)\}$ is monotone! (it.wikipedia.org/wiki/Lemma_di_Dini)


text:
# Transforming vectors to coordinate vectors

Let $X_1,\dots,X_n$ be n vector fields on an open subset $U$ of a manifold of dimension $n$ Suppose that at $p\in U$, the vectors $(X_1)_p,\dots,(X_n)_p$ are linearly indipendent. would any one say in detail how I will show that there is a chart $(V,x^1,\dots,x^n)$ about $p$ such that $(X)_p=(\partial/\partial x^i)_p$ for all $i=1,\dots,n$, here I use superscript for coordinates like $x^1,\dots,x^n$

-

By the Frobenius theorem, given a local basis $X_i$ of $TM$, there exists a chart $x_i$ with $X_i = \partial_i$ if and only if the for all $i,j$, $[X_i,X_j]=0$.
Basically, $[X,Y]$ measures the difference between infinitesmially flowing out $X$, then over on $Y$, versus infinitesimally flowing out $Y$, then flowing over on $X$. In order to have coordinates, the two must always agree, otherwise the "location" of a point is not well-defined - getting there from the origin by flowing out $X$, then $Y$, would result in a different position flowing out $Y$ from $X$.


text:
Properties of Complex Numbers

We will discuss here about the different properties of complex numbers.

1. When a, b are real numbers and a + ib = 0 then a = 0, b = 0

Proof:

According to the property,

a + ib = 0 = 0 + i  0,

Therefore, from the definition of equality of two complex numbers we conclude that, x = 0 and y = 0.

2. When a, b, c and d are real numbers and a + ib = c + id then a = c and b = d.

Proof:

According to the property,

a + ib = c + id and a, b, c and d are real numbers.

Therefore, from the definition of equality of two complex numbers we conclude that, a = c and b = d.

3. For any three the set complex numbers z$$_{1}$$, z$$_{2}$$ and z$$_{3}$$ satisfies the commutative, associative and distributive laws.

(i) z$$_{1}$$ + z$$_{2}$$ = z$$_{2}$$ + z$$_{1}$$ (Commutative law for addition).

(ii) z$$_{1}$$ z$$_{2}$$ = z$$_{2}$$ z$$_{1}$$ (Commutative law for multiplication).

(iii) (z$$_{1}$$ + z$$_{2}$$) + z$$_{3}$$ = z$$_{1}$$ + (z$$_{2}$$ + z$$_{3}$$) (Associative law for addition)

(iv) (z$$_{1}$$z$$_{2}$$)z$$_{3}$$ = z$$_{1}$$(z$$_{2}$$z$$_{3}$$) (Associative law for multiplication)

(v) z$$_{1}$$(z$$_{1}$$ + z$$_{3}$$) = z$$_{1}$$z$$_{2}$$ + z$$_{1}$$z$$_{3}$$ (Distributive law).

4. The sum of two conjugate complex numbers is real.

Proof:

Let, z = a + ib (a, b are real numbers) be a complex number. Then, conjugate of z is $$\overline{z}$$ = a - ib.

Now, z + $$\overline{z}$$ = a + ib + a - ib = 2a, which is real.

5. The product of two conjugate complex numbers is real.

Proof:

Let, z = a + ib (a, b are real number) be a complex number. Then, conjugate of z is $$\overline{z}$$ = a - ib.

$$\overline{z}$$ = (a + ib)(a - ib) = a$$^{2}$$ - i$$^{2}$$b$$^{2}$$ = a$$^{2}$$ + b$$^{2}$$, (Since i$$^{2}$$ = -1), which is real.

Note: When z = a + ib then |z| = $$\sqrt{a^{2} + b^{2}}$$and, z$$\overline{z}$$ = a$$^{2}$$ + b$$^{2}$$

Hence, $$\sqrt{z\overline{z}}$$ = $$\sqrt{a^{2} + b^{2}}$$

Therefore, |z| = $$\sqrt{z\overline{z}}$$

Thus, modulus of any complex number is equal to the positive square root of the product of the complex number and its conjugate complex number.

6. When the sum of two complex numbers is real and the product of two complex numbers is also real then the complex numbers are conjugate to each other.

Proof:

Let, z$$_{1}$$ = a + ib and z$$_{2}$$ = c + id be two complex quantities (a, b, c, d and real and b ≠ 0, d ≠0).

According to the property,

z$$_{1}$$ + z$$_{2}$$ = a+ ib + c + id = (a + c) + i(b + d) is real.

Therefore, b + d = 0

⇒ d = -b

And,

z$$_{1}$$z$$_{2}$$ = (a + ib)(c + id) = (a + ib)(c +id) = (ac – bd) + i(ad + bc) is real.

Therefore, ad + bc = 0

⇒ -ab + bc = 0, (Since, d = -b)

⇒ b(c - a) = 0

⇒ c = a (Since, b ≠ 0)

Hence, z$$_{2}$$ = c + id = a + i(-b) = a - ib = $$\overline{z_{1}}$$

Therefore, we conclude that z$$_{1}$$ and z$$_{2}$$ are conjugate to each other.

7. |z$$_{1}$$ + z$$_{2}$$| ≤ |z$$_{1}$$| + |z$$_{2}$$|, for two complex numbers z$$_{1}$$ and z$$_{2}$$.


text:
# Logistic regression BIC: what's the right N?

TL;DR: Which $$N$$ is correct for BIC in logistic regression, the aggregated binomial or Bernoulli $$N$$?

Suppose I have a data set to which I'd like to apply logistic regression. For the sake of example, suppose there are $$j=5$$ groups with $$m=100$$ participants each, for a total $$n=500$$. The outcome is 0 or 1. For example, the following data set (R code):

library(dplyr)
library(tidyr)

set.seed(45)
d <- tibble(y = rbinom(500, 1, .5),
x = factor(rep(LETTERS[1:5], each = 100)))

There are two ways I can represent this: as is, above, treating every observation as a Bernoulli random variable, or aggregating observations within groups and treating each observation as Binomial. The number of rows in the data set will be 500 in the first instance, and 5 in the second.

I can construct the aggregated data set:

d %>%
group_by(x, y) %>%
summarise(n = n()) %>%
rename(f = 0, s = 1) %>%
mutate(n = s + f) -> d_agg

I can then fit the logistic regression using both data sets in R:

g_bern  <- glm(y ~ x,          data=d,     family=binomial)
g_binom <- glm(cbind(s,f) ~ x, data=d_agg, family=binomial)

UPDATE 2: We now fit the intercept only models:

g_bern0  <- glm(y ~ 1,          data=d,     family=binomial)
g_binom0 <- glm(cbind(s,f) ~ 1, data=d_agg, family=binomial)

and compute the AIC:

> AIC(g_bern)
# [1] 694.6011
> AIC(g_binom)
# [1] 35.22172

which of course differ by a constant

2*sum(lchoose(d_agg$$n, d_agg$$s))  # [1] 659.3794

as expected (see: Logistic Regression: Bernoulli vs. Binomial Response Variables).

However, the BICs differ by that constant AND a factor that depends on the "number of observations", and the number of observations differ in each:

> BIC(g_bern)
# [1] 715.6742
> BIC(g_binom)
# [1] 33.26891
> nobs(g_bern)
# [1] 500
> nobs(g_binom)
# [1] 5

Just to confirm, we can recalculate BIC for both:

> -2*logLik(g_bern) + attr(logLik(g_bern),"df")*log(nobs(g_bern))
# 'log Lik.' 715.6742 (df=5)
> -2*logLik(g_binom) + attr(logLik(g_binom),"df")*log(nobs(g_binom))
# 'log Lik.' 33.26891 (df=5)

and indeed the only place these two numbers differ is $$N$$.

UPDATE 2: When we try to assess the factor x, we see a disagreement that is ONLY attributable to the number of observations:

> BIC(g_bern0) - BIC(g_bern)
# [1] -17.66498
> BIC(g_binom0) - BIC(g_binom)
# [1] 0.7556999

UPDATE 2: As expected, the AICs are consistent:

> AIC(g_bern0) - AIC(g_bern)
# [1] -0.8065485
> AIC(g_binom0) - AIC(g_binom)
# [1] -0.8065485

This surprises me, since I would think that R would "know" which of the two to use to prevent ambiguity. It has the same information in both cases.

Which one is "right"? Or is BIC really this arbitrary?

UPDATE: I am not trying to compare the Bernoulli to the Binomial model. This is just a toy example. I have a set of comparisons where it matters which setup I use, because the penalties for $$N$$ are different. I have two sets of model comparisons and the winning model changes based on the $$N$$ penalty, even though these appear to me to be the same sets of models.

UPDATES 2 and 3: Added the comparisons to the intercept-only model and changed random seed to get a sign difference in the BIC.

The BIC (and the AIC) are relative measures for comparing models. However, it makes no sense to compare what is otherwise the same model between using an aggregated vs. a disaggregated response. Nor would it make sense to compare models that would otherwise be different (e.g., different regressors), but where one model uses an aggregated response and the other model uses a disaggregated version of the response. As long as the two models being compared both represent the response variable in the same format, everything will be fine. Note that the two formats are ultimately equivalent—they contain the same information and mostly just look different on the outside, see: Input format for response in binomial glm in R.

• Just to clarify: I am not trying to compare g_bern to g_binom. This is a toy example. I have an application in which this penalty matters for which model wins. So everything is not fine in the sense that they are not equivalent. That is the point. (see my update) – Salad dressing Mar 10 at 8:56
• Then you need to describe the actual situation you are facing, not some toy example that differs. XY questions often lead to answers that don't address what the asker really needs to know. – gung Mar 10 at 13:47
• I added an update showing that the comparisons with the intercept-only model are inconsistent between the approaches due to the number of observations being different. My question is which of the two seemingly equivalent approaches is "correct". – Salad dressing Mar 10 at 21:24
• @Saladdressing, I don't follow your update. Where is g_bern0, eg, defined? If the idea is that it was supposed to be an intercept-only model, I don't see a problem. The actual numbers of the BIC don't matter. It's just a relative measure. In both cases (ie, g_bern0, & g_binom0), the difference is negative, implying the same preference (for the intercept-only model). There is no inconsistency. – gung Mar 11 at 2:01
• The difference in BIC between the two comparisons was an order of magnitude, which is huge on a logarithmic value such as BIC. And these are supposed to be the same models. But anyway, I incremented the seed. Now there is a sign inconsistency between the two BIC comparisons. I cannot see how "the two formats are ultimately equivalent—they contain the same information and mostly just look different on the outside" could possibly be true given that one BIC is -18, and the other is 1. This is a staggering difference. – Salad dressing Mar 11 at 14:43

Interesting question! Coming at this from an applied setting, I think you need to remember that both BIC and AIC are measures of relative model fit.

In other words, these measures don't tell you much when you examine them for a single model, but can help you to select an appropriate model among a set of competing models. In particular:

1. If your goal is to find the 'best' among those competing models for prediction of the outcome variable, then select the model with the lowest AIC value;
2. If your goal is to find the 'best' among those competing models for understanding and describing the effects of the predictor variables included in the model on the outcome variable, then select the model with the lowest BIC value.

In defining your set of competing models, you would have to make sure the models follow the same conceptual framework. Thus, you would either compare several binomial logistic regression models or several binary logistic models, but not a mixture of both. (It is important to compare like with like, otherwise you won't know if a model won the competition based on its own merits or simply because you changed the model specification/fitting procedure.)

From this perspective, the only thing that matters is that R is consistent when computing the AIC and BIC across models of the same type (e.g., binomial logistic regression models).

Just to clarify: g_bern is a binary logistic regression model, whereas g_binom is a binomial logistic regression model. While they both model the probability of success in one trial, you wouldn't mix together variations of these models when defining your set of competing models (for the reasons explained above and also covered by @gung).

• Please see my update. Just to clarify: I am not trying to compare g_bern to g_binom. This is a toy example. – Salad dressing Mar 10 at 8:57


text:
# The remainder when 1010 + 10100 + 101000 + . . . . . . + 101000000000 is divided by 7 is

• 10
• 21
• 32
• 45
Explanation:-

Solution:
Number of terms in the series = 10.
(We can get it easily by pointing the number of zeros in power of terms.
In 1st term number of zero is 1, 2nd term 2, and 3rd term 3 and so on.)
$\begin{array}{rl}& \frac{{10}^{10}}{7},\phantom{\rule{thinmathspace}{0ex}}\text{Written}\phantom{\rule{thinmathspace}{0ex}}\text{as},\\ & \frac{{\left(7+3\right)}^{\left(4×2+2\right)}}{7}\\ & \text{The}\phantom{\rule{thinmathspace}{0ex}}\text{remainder}\phantom{\rule{thinmathspace}{0ex}}\text{will}\phantom{\rule{thinmathspace}{0ex}}\text{depend}\phantom{\rule{thinmathspace}{0ex}}\text{on},\\ & \frac{{3}^{2}}{7}\\ & \text{So,}\phantom{\rule{thinmathspace}{0ex}}\text{remainder}\phantom{\rule{thinmathspace}{0ex}}\text{will}\phantom{\rule{thinmathspace}{0ex}}\text{be}\phantom{\rule{thinmathspace}{0ex}}2\\ & \frac{{10}^{1000}}{7},\phantom{\rule{thinmathspace}{0ex}}\text{remainder}=2\\ & \frac{{10}^{10000}}{7},\phantom{\rule{thinmathspace}{0ex}}\text{remainder}=1\\ & \text{So, we get alternate 2 and 1 as remainder, five times each}\text{.}\\ & \text{So, required remainder is given by}\\ & \frac{\left(2+1+2+1+2+1+2+1+2+1\right)}{7}\\ & =\frac{15}{7}\end{array}$

", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "
Solution:
Number of terms in the series = 10.
(We can get it easily by pointing the number of zeros in power of terms.
In 1st term number of zero is 1, 2nd term 2, and 3rd term 3 and so on.)
$\begin{array}{rl}& \frac{{10}^{10}}{7},\phantom{\rule{thinmathspace}{0ex}}\text{Written}\phantom{\rule{thinmathspace}{0ex}}\text{as},\\ & \frac{{\left(7+3\right)}^{\left(4×2+2\right)}}{7}\\ & \text{The}\phantom{\rule{thinmathspace}{0ex}}\text{remainder}\phantom{\rule{thinmathspace}{0ex}}\text{will}\phantom{\rule{thinmathspace}{0ex}}\text{depend}\phantom{\rule{thinmathspace}{0ex}}\text{on},\\ & \frac{{3}^{2}}{7}\\ & \text{So,}\phantom{\rule{thinmathspace}{0ex}}\text{remainder}\phantom{\rule{thinmathspace}{0ex}}\text{will}\phantom{\rule{thinmathspace}{0ex}}\text{be}\phantom{\rule{thinmathspace}{0ex}}2\\ & \frac{{10}^{1000}}{7},\phantom{\rule{thinmathspace}{0ex}}\text{remainder}=2\\ & \frac{{10}^{10000}}{7},\phantom{\rule{thinmathspace}{0ex}}\text{remainder}=1\\ & \text{So, we get alternate 2 and 1 as remainder, five times each}\text{.}\\ & \text{So, required remainder is given by}\\ & \frac{\left(2+1+2+1+2+1+2+1+2+1\right)}{7}\\ & =\frac{15}{7}\end{array}$
", "dateCreated": "7/24/2019 10:09:12 AM" } }


text:
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panchorivasf
@panchorivasf
Hi everyone! Like many of you, I'm a newcomer to AP so I come with few silly questions for the team:
1) How can I script AP to change the time window at which it calculates the AIs? I have a bunch of full-day recordings with a non-continuous recording schedule: 1min-on / 9min-off. Obviously, when I run AP for a full day of recordings, it shows a 2.5 long spectrogram (or around that), which is not very useful. So I wonder if I can set the AI calculation to 1 sec per pixel.
(above I meant 2.5 hour-long spectrogram)
panchorivasf
@panchorivasf
2) What happens if I want to load a full day of continuous recordings that are already in 1 min chunks? This is the default for Audiomoths and I generally prefer to use this schedule because it allows me to fast scanning with Adobe Audition spectrogram view. By the moment, I've been putting all recordings together in a single file before loading into AP, but it seems redundant that the program will cut it into 1 min chunks again.
(sorry if that was too silly)
3) Have someone out there plotted temperature (and/or humidity, light metrics, etc.) over a false-color spectrogram? That would be amazing!
Anthony Truskinger
@atruskie

hi @panchorivasf ,

1) We call that configuration value IndexCalculationDuration. See here https://github.com/QutEcoacoustics/audio-analysis/blob/master/src/AnalysisConfigFiles/Towsey.Acoustic.yml#L22-L27

2) Just because the audiomoths default to 1-minute chunks doesn't mean that's a good size audio file. Record in segments that suit your study. The overhead in metadata and filesystem load for thousands of small files can be significant.

1. loop through each file, calculate indices for each file
2. use concatenateindexfiles to stitch the results together

Here is an example script https://github.com/QutEcoacoustics/audio-analysis/blob/master/scripts/indices_and_concat.ps1 , and some guidance from our documentation: https://ap.qut.ecoacoustics.info/technical/commands/concatenate_index_files.html https://ap.qut.ecoacoustics.info/basics/scripting.html

This process can be extremely inefficient for lots of small files. It's something we're looking to improve upon. See QutEcoacoustics/audio-analysis#378

3) Michael (@towsey) did plot day phases. The middle FCS in slide 13 has day phases attached in https://research.ecosounds.org/research/eadm-towsey/long-duration-audio-recordings-of-the-environment#slide-13-cross-site-comparison-varying-latitudes.

As for temps, I don't think so

panchorivasf
@panchorivasf
@atruskie I was reading the ConfigFiles parameters, and this warning puzzled me: # IMPORTANT NOTE: FC spectrograms are produced only IF the above IndexCalculationDuration := 60.0. So if I reduce the ICD, there will be no FC spectrogram output? or is that a warning for when you want to change FCS's color parameters only?
Anthony Truskinger
@atruskie

@panchorivasf :

@atruskie Awesome! I'll navigate through those commands and see what happens. Did Michael attach the day phases manually (e. g. using some graphics software)?

He did it in AP - but we removed that code, it only worked in one area and wasn't very good too

You can attach any image you want simply by placing it underneath the image. For a IndexCaculationDuration of 60, each column of pixel is 1 minute long. So to produce a graph that is 24 hours long, make an image 1440px wide

Anthony Truskinger
@atruskie

Ah, that's a holdover from past technicalities. It used to be we couldn't do too much at one time or else we'd run out of memory. Capping the rendering resolution to 60 kept the indices generation fast.

Anyway, generate indices first with audio2csv then use DrawLongDurationSpectrograms to make the images

panchorivasf
@panchorivasf
Awesome, thank you @atruskie !
Francisco Rivas Fuenzalida
@fcorivasf_gitlab
Hi again! I don't know how does the workflow goes to make the LDSs afterwards. I'm typing: C:\AP\AnalysisPrograms.exe DrawLongDurationSpectrograms
(...) and then I guess I should give the path to the csv file right?
Anthony Truskinger
@atruskie

The first thing to do is use the --help option to see what arguments the command takes

AnalysisPrograms.exe DrawLongDurationSpectrograms --help

Then see what happens

Francisco Rivas Fuenzalida
@fcorivasf_gitlab
Thanks I did. The thing I don't get yet is how many arguments are required to make the spectrogram.
Anthony Truskinger
@atruskie

It's been a while - so I don't know for sure!
But the simple answer is as many as needed 😂

Looking at the help docs, probably at least -i, -o, -ip, -fcs

Francisco Rivas Fuenzalida
@fcorivasf_gitlab
ok I'll keep trying, thanks!
when I typed the path for -fcs it gives me an error message saying it was waiting for a .yml instead of a .csv
Anthony Truskinger
@atruskie
mmm bad documentation - i'll fix that
But it is looking for a config file, you can infer that from the rest of the description -fcs|--false-colour-spectrogram-config <FALSE_COLOUR_SPECTROGRAM_CONFIG>
it'll be the ConfigFiles/SpectrogramFalseColourConfig.yml one
Updated, you'll see it inlcuded in Monday's automated release of AP.exe QutEcoacoustics/audio-analysis@f78c09a
Francisco Rivas Fuenzalida
@fcorivasf_gitlab
Let me see if I understand. The actual file from which AP will make the LDS must be given after "-i"?
Anthony Truskinger
@atruskie

well the directory, yeah. The output of indices generation is the input to image drawing

generate indices ➡ draw false colour spectrogram

Francisco Rivas Fuenzalida
@fcorivasf_gitlab
ok, I'll see what happens. Thank you!
is the order of the arguments important?
Anthony Truskinger
@atruskie

there is distinction betwen arguments and options.

arguments: yes, order is important. Arguments are values for which you don't have to put their name in front. Example: AnalysisPrograms.exe audio2csv C:\Audio Towsey.Acoustic.yml C:\output <-- there are three arguments there, each separated by a space

options: order is not important. Options are always prefixed with their name (like -i or --input-data-directory) and then the value. Example: --input-data-directory C:\indices\

Francisco Rivas Fuenzalida
@fcorivasf_gitlab
gotcha! I was confused when you said I should enter --help to see what arguments the command takes... thanks for explaining!
Anthony Truskinger
@atruskie

yeah --help should be available on every command. Even though I've written most of AP.exe, I still regularly forget things. --help is the first thing I do everytime.

Some commands will take arguments, some options, and some both. Techincally an option is a special type of argument (hence my confusing statement)

Francisco Rivas Fuenzalida
@fcorivasf_gitlab
gotcha. Other question: when I enter -i, should I include a file name at the end of the directory?
Anthony Truskinger
@atruskie
Definitely a directory. I think also it needs Towsey.Acoustic appended. E.g. C:\Indices\IndicesForFileA\Towsey.Acoustic
Francisco Rivas Fuenzalida
@fcorivasf_gitlab
within -i?
or that is -ip?
or -fcs?
Francisco Rivas Fuenzalida
@fcorivasf_gitlab
I'm here:
C:\AP\AnalysisPrograms.exe DrawLongDurationSpectrograms -i D:\PhD\TANZANIA\IndicesOutput\Towsey.Acoustic\S4A03863 -O D:\PhD\TANZANIA\IndicesOutput\Towsey.Acoustic\S4A03863 -ip C:\AP\ConfigFiles\IndexPropertiesConfig.yml
Anthony Truskinger
@atruskie

Your directory structure looks a bit weird. In D:\PhD\TANZANIA\IndicesOutput\Towsey.Acoustic\S4A03863 is there a Towsey.Acoustic folder?

Does that command work?

Other than that, it's the right format

Francisco Rivas Fuenzalida
@fcorivasf_gitlab
I've run that without the Towsey.Acoustic and it gives an error message: FATAL - Unhandled exception ->
13 replies
There is the Towsey.Acoustic folder created by AP to store the AIs
I've made the \S4A03863 to separate the data from different sensors
So within the Towsey.Acoustic folder there is no file but other three folders
Abram Fleishman
@abfleishman
I have been using the Towsey.Acoustic config file with audio2csv to calculate acoustic indices for short (1 minute) files. It works well; however, it generates a bunch of other analyses that I am not using and I now want to unleash it on ~10 TB of 1-minute files. Essentially I am interested in only creating this file for each sound file: *__Towsey.Acoustic.Indices.csv. Is this possible? can you point me in the right direction? Thanks for a great tool!
Anthony Truskinger
@atruskie

@abfleishman the short answer is don't do this.

AP.exe is not made for processing 1-minute files - it will perform slowly and will be quite inefficient. 1-minute files are a bad choice for storing and collecting data, especially for consecutive minutes. Unfortunately, people keep doing this, so we intend to add support for it (QutEcoacoustics/audio-analysis#378); however, it will be a while before that is implemented.

With the warning out of the way: it's possible. We've done it before, on datasets larger than 10TB.

, it generates a bunch of other analyses

Slightly incorrect. It generates other sorts of indices, which we call spectral indices. They are very much acoustic indices though.

Currently, we do not have the options to calculate just a subset of the indices. It's been suggested a few times and when I went searching for the relevant feature request, I found your name mentioned!

QutEcoacoustics/audio-analysis#240

All I can say is sorry. We've been under a lot of pressure. For our typical use case (2, or 6-hour long files) the default settings make sense and aren't that annoying, even when we don't need a subset of the files which makes it a low priority.

I'd recommend just deleting the files you don't need after each loop. It'd be worthwhile keeping some of the metadata (like the index generation data json).

Abram Fleishman
@abfleishman
@atruskie Thanks for your reply. I thought I had asked a similar question a few years back but searched for me github handle and didn't find anything. looks like it came from an email?! I understand your caution away from short files, however, we find that consecutive minutes are often highly autocorrelated and thus do not provide much additional biological information. Also, we often can visit sites infrequently and thus need to use a duty cycle of 1 min every 5 or 10 to extend deployment periods (both battery and memory). I have used your tools on 1 minute files successfully in the past
Anthony Truskinger
@atruskie

@abfleishman yeah, I get there are plenty of valid reasons to sample data. The issue I keep running into is people doing it by default, especially for consecutive minutes. Small files create huge strain on filesystems... and I'm over here trying to write software that works for not just their project, but every project we get all at once.

FWIW, we've been collecting data on continuous schedules by default. With our new sensors service time is every 6 or 12 months.

And yeah, AP.exe has no obvious issue working with short files, but audio2csv in particular expects it. It does a bunch of stuff like duration checking, chunking, minute alignment, and outputting data files in shapes that really don't make sense for short files. It's --parallel option is also unused.

Anyway /rant :-)

My contract is changing soon and I'll be back to working on AP.exe more regularly. Hopefully I'll be able to provide some good news soon!

Abram Fleishman
@abfleishman
Thanks for the info, I will key my eye on the repo and look forward to seeing it continue to evolve
Francisco Rivas Fuenzalida
@fcorivasf_gitlab
Hi @atruskie ! I wonder if there is an option to show the frequency values outside the FCS. They mask the midnight events and they don't look very well aesthetically. Thank you!
Anthony Truskinger
@atruskie

@fcorivasf_gitlab no there isn't. Sounds like a good feature request? Do you want to add it the feature request to the issue tracker?

Historically, we intended the images to sit side by side for quick and dirty alignments without any padding.

We're encountering cases now we're people are looking for prettier images and aesthetic options like this are becoming more important

mitesser
@mitesser
Dear @atruskie, seems that I missed it in the documentation: Is there a list of descriptions for all the index abbreviations used in the csv spectral output files *.Acoustic.ACI, BGN, CVR, DIF, ENT, EVN, ...., SPT, SUM? My specific aim is to find one that represents (or could be used as starting point for calculating) simple db mean for each frequeny bin (per minute).
Anthony Truskinger
@atruskie

@mitesser no, not currently. The best resource is Towsey's whitepaper on the topic - see https://eprints.qut.edu.au/110634/

The documentation is a much newer (part-time labour of love) than the indices and it is nowhere near finished. We aim to merge that white paper into our documentation.

The index you're looking for is PMN (power minus noise). The true power could be obtained by doing PMN + BGN if you need it (I'll double check that and get back to you)


text:
# Radius of Convergence for an infinit sum

Given the following infinite sum,

∞∑n=1xn√n+1\sum _{ n=1 }^{ \infty }{ \frac { x^n }{\sqrt{n+1}} }

a) Find the radius of convergence? Find for what values of ρ\rho it is convergent and divergent?

b) Find the sum for x=−1x=-1 with an error of highest 0.010.01, by using the sum of a finite sum with of a suitable number of variables.

My Approach

So what I have done so far is the following,

a) I used the ratio to determine the radius of convergence,

|an+1an||\frac{a_{n+1}}{a_n}|

|xn+1√(n+1)+1xn√n+1||\frac{\frac { x^{n+1} }{\sqrt{(n+1)+1}} }{\frac { x^n }{\sqrt{n+1}} }|

|√n+1√n+2×x||\frac{\sqrt{n+1}}{\sqrt{n+2}} \times x|

As n goes towards infinity, we get the following,

|x||x|

Hence therefore the radius of convergence, ρ=1\rho=1.

Now if

x=ρ=1x=\rho=1, then the sum is divergent because it is not less than 1.

x=−ρ=1x=-\rho=1, then the sum is convergent because it is less than 1.

(Is it correct how I have solve part a)?

b) For this part, I am not sure even how to start. Because how am I suppose to determine a finite sum to find the sum for the error 0.01. Any hint or help will be great.

=================

=================

2

=================

Hint for (b):

Observe
∞∑n=1(−1)n√n=N∑n=1(−1)n√n+∞∑n=N+1(−1)n√n\begin{align}
\sum^\infty_{n=1} \frac{(-1)^n}{\sqrt{n}}=\sum^N_{n=1} \frac{(-1)^n}{\sqrt{n}}+\sum^\infty_{n=N+1} \frac{(-1)^n}{\sqrt{n}}
\end{align}
which means
|∞∑n=1(−1)n√n−N∑n=1(−1)n√n|= |1√N+1−1√N+2+1√N+3−1√N+4+…|= |√N+2−√N+1√(N+2)(N+1)|+|√N+3−√N+2√(N+3)(N+2)|+…≤ 1√N+2(N+1)+1√N+3(N+2)+…≤ ∫∞Ndx(x+1)√x+2≤∫∞Ndxx√x.\begin{align}
\left|\sum^\infty_{n=1} \frac{(-1)^n}{\sqrt{n}}-\sum^N_{n=1} \frac{(-1)^n}{\sqrt{n}} \right| =&\ \left| \frac{1}{\sqrt{N+1}}-\frac{1}{\sqrt{N+2}}+\frac{1}{\sqrt{N+3}}-\frac{1}{\sqrt{N+4}}+\ldots \right|\\
=&\ \left|\frac{\sqrt{N+2}-\sqrt{N+1}}{\sqrt{(N+2)(N+1)}} \right|+\left|\frac{\sqrt{N+3}-\sqrt{N+2}}{\sqrt{(N+3)(N+2)}} \right|+\ldots\\
\leq&\ \frac{1}{\sqrt{N+2}(N+1)}+\frac{1}{\sqrt{N+3}(N+2)}+\ldots \\
\leq&\ \int^\infty_{N} \frac{dx}{(x+1)\sqrt{x+2}} \leq \int^\infty_{N} \frac{dx}{x\sqrt{x}}.
\end{align}

Evaluate the last integral to get a bound on the error. Then see for what NN you will have an error of at most .01.01.

Edit: I have used the fact that
√N+2−√N+1= √N+2+√N+1√N+2+√N+1[√N+2−√N+1]= 1√N+2+√N+1≤1√N+1.\begin{align}
\sqrt{N+2}-\sqrt{N+1} =&\ \frac{\sqrt{N+2}+\sqrt{N+1}}{\sqrt{N+2}+\sqrt{N+1}}[\sqrt{N+2}-\sqrt{N+1}] \\
=&\ \frac{1}{\sqrt{N+2}+\sqrt{N+1}} \leq \frac{1}{\sqrt{N+1}}.
\end{align}

Thank You. So that means I have to solve (integral)=0.01 and then solve for N, right?
– captainavenger96
Oct 20 at 20:07

@captainavenger96 exactly â€“ you solve the integral in terms of NN and ∞\infty (which should disappear) and you’ll be left with a function in terms of NN which is equal to 0.010.01, which you can then solve 🙂
– Skeleton Bow
Oct 20 at 20:10

1

Great. Thank you once again for your help 🙂
– captainavenger96
Oct 20 at 20:11

1

I have used the fact that √n+1−√n≤1√n\sqrt{n+1}-\sqrt{n} \leq \frac{1}{\sqrt{n}}.
– Jacky Chong
Oct 20 at 21:48

1

Which follows from √n+1+√n√n+1+√n(√n+1−√n)\frac{\sqrt{n+1}+\sqrt{n}}{\sqrt{n+1}+\sqrt{n}}(\sqrt{n+1}-\sqrt{n}).
– Jacky Chong
Oct 20 at 21:49

You’re almost there for a.

Yes, the radius of convergence is 11. You could also use the Cauchy-Hadamard formula, as told to me by a great mathematician by the name Don Antonio.

When x=1x=1, the sum becomes

∞∑n=11√n+1\sum\limits_{n=1}^{\infty}{\frac{1}{\sqrt{n+1}}}

This diverges according to the Limit Comparison Test with 1n0.5\frac{1}{n^{0.5}}.

When x=−1x=-1, it is

∞∑n=1(−1)n√n+1\sum\limits_{n=1}^{\infty}{\frac{(-1)^n}{\sqrt{n+1}}}

This converges according to the Alternating Series Test, as it a) alternates and b) is decreasing (try looking at the derivative of f(n)=|un|f(n)=\left|{u_n}\right| and see if the function is increasing or decreasing!)

I don’t know about b, sorry!

Thank You for your time and help!! 🙂
– captainavenger96
Oct 20 at 20:08

2

No problem! I’m glad I could be of help. Also if you choose an answer to this question, please choose the other guy, he did most of the helping 😉
– Skeleton Bow
Oct 20 at 20:10


text:
Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1349

 Title: Classiﬁcation of Smoking Cessation Status Using Various Data Mining Methods Authors: Kartelj, Aleksandar Keywords: Data MiningClassiﬁcationInduction Learning Issue Date: 2010 Publisher: Bulgarian Academy of Sciences - National Committee for Mathematics Citation: Mathematica Balkanica New Series, Vol. 24, Fasc 3-4 (2010), 199p-205p Abstract: This study examines diﬀerent approaches of binary classiﬁcation applied to the prob- lem of making distinction between former and current smokers. Prediction is based on data collected in national survey performed by the National center for health statistics of America in 2000. The process consists of two essential parts. The ﬁrst one determines which attributes are relevant to smokers status, by using methods like basic genetic algorithm and diﬀerent evaluation functions [1]. The second part is a classiﬁcation itself, performed by using methods like logistic regression, neural networks and others [2]. Solving these types of problems has its real contributions in decision support systems used by some health institutions. Description: AMS Subj. Classiﬁcation: 62P10, 62H30, 68T01 URI: http://hdl.handle.net/10525/1349 ISSN: 0205-3217 Appears in Collections: Mathematica Balkanica New Series, Vol. 24, 2010, Fasc. 3-4

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text:
### Computing the optimal strategy to commit to

In multiagent systems, strategic settings are often analyzed under the assumption that the players choose their strategies simultaneously. However, this model is not always realistic. In many settings, one player is able to commit to a strategy before the other player makes a decision. Such models are synonymously referred to as leadership, commitment, or Stackelberg models, and optimal play in such models is often significantly different from optimal play in the model where strategies are selected simultaneously.The recent surge in interest in computing game-theoretic solutions has so far ignored leadership models (with the exception of the interest in mechanism design, where the designer is implicitly in a leadership position). In this paper, we study how to compute optimal strategies to commit to under both commitment to pure strategies and commitment to mixed strategies, in both normal-form and Bayesian games. We give both positive results (efficient algorithms) and negative results (NP-hardness results).

[1]  A. Cournot Researches Into The Mathematical Principles Of The Theory Of Wealth , 1898 .

[2]  J. Neumann Zur Theorie der Gesellschaftsspiele , 1928 .

[3]  H. Stackelberg,et al.  Marktform und Gleichgewicht , 1935 .

[4]  J. Nash Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[5]  O. H. Brownlee,et al.  ACTIVITY ANALYSIS OF PRODUCTION AND ALLOCATION , 1952 .

[6]  Steven Vajda,et al.  Games and Decisions , 1959 .

[7]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[8]  D. Knuth,et al.  A note on strategy elimination in bimatrix games , 1988 .

[9]  Eitan Zemel,et al.  Nash and correlated equilibria: Some complexity considerations , 1989 .

[10]  D. Koller,et al.  The complexity of two-person zero-sum games in extensive form , 1992 .

[11]  Eitan Zemel,et al.  The Complexity of Eliminating Dominated Strategies , 1993, Math. Oper. Res..

[12]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[13]  D. Koller,et al.  Efficient Computation of Equilibria for Extensive Two-Person Games , 1996 .

[14]  Michael L. Littman,et al.  Graphical Models for Game Theory , 2001, UAI.

[15]  Christos H. Papadimitriou,et al.  Algorithms, Games, and the Internet , 2001, ICALP.

[16]  Moshe Tennenholtz,et al.  Local-Effect Games , 2003, IJCAI.

[17]  Peter Stone,et al.  A polynomial-time nash equilibrium algorithm for repeated games , 2003, EC '03.

[18]  Aranyak Mehta,et al.  Playing large games using simple strategies , 2003, EC '03.

[19]  Vincent Conitzer,et al.  Complexity Results about Nash Equilibria , 2002, IJCAI.

[20]  A. Cournot Mathematical Principles of the Theory of Wealth , 2004 .

[21]  Kevin Leyton-Brown,et al.  Computing Nash Equilibria of Action-Graph Games , 2004, UAI.

[22]  B. Stengel,et al.  Leadership with commitment to mixed strategies , 2004 .

[23]  Yoav Shoham,et al.  Run the GAMUT: a comprehensive approach to evaluating game-theoretic algorithms , 2004, Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems, 2004. AAMAS 2004..

[24]  Vincent Conitzer,et al.  A Generalized Strategy Eliminability Criterion and Computational Methods for Applying It , 2005, AAAI.

[25]  Vincent Conitzer,et al.  Mixed-Integer Programming Methods for Finding Nash Equilibria , 2005, AAAI.

[26]  Vincent Conitzer,et al.  Complexity of (iterated) dominance , 2005, EC '05.

[27]  Yoav Shoham,et al.  Simple search methods for finding a Nash equilibrium , 2008, Games Econ. Behav..


text:
• # question_answer Choose the mirror image of the given figure. A)          B)        C)            D)        E) None of these

Solution :

Explanation Option [a] is correct because this is the horizontally inverted figure of the actual figure. Let us see: Actual figure: Option [a]: Clearly, in option [a], the L.H.S. is the R.H.S. of the actual figure and the R.H.S. is the L.H.S. of the actual figure. Hence, option [a] is the mirror image of the given figure. Rest of the options is incorrect because of the correctness of option [a].

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text:
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text:
## Elementary Technical Mathematics

$$4.66\times 10^{13}.$$
We multiply the two numbers as follows: $$(4500)(69,000)(150,000)=(4.5\times 10^3)(6.9\times 10^4)(1.5\times 10^5) \\=46.575\times 10^{12}=4.66\times 10^{13}.$$


text:
# Multiplication of Real and Imaginary Parts

## Theorem

Let $w, z \in \C$ be complex numbers.

$(1)$ If $w$ is wholly real, then:

$\map \Re {w z} = w \, \map \Re z$

and:

$\map \Im {w z} = w \, \map \Im z$

$(2)$ If $w$ is wholly imaginary, then:

$\map \Re {w z} = -\map \Im w \, \map \Im z$

and:

$\map \Im {w z} = \map \Im w \, \map \Re z$

Here, $\map \Re z$ denotes the real part of $z$, and $\map \Im z$ denotes the imaginary part of $z$.

## Proof

Assume that $w$ is wholly real.

Then:

 $\ds w z$ $=$ $\ds \map \Re w \, \map \Re z - \map \Im w \, \map \Im z + i \paren {\map \Re w \, \map \Im z + \map \Im w \, \map \Re z}$ Definition of Complex Multiplication $\ds$ $=$ $\ds w \, \map \Re z + i w \, \map \Im z$ as $\map \Re w = w$ and $\map \Im w = 0$

This equation shows that $\map \Re {w z} = w \, \map \Re z$, and $\map \Im {w z} = w \, \map \Im z$.

This proves $(1)$.

Now, assume that $w$ is wholly imaginary.

Then:

 $\ds w z$ $=$ $\ds \map \Re w \, \map \Re z - \map \Im w \, \map \Im z + i \paren {\map \Re w \, \map \Im z + \map \Im w \, \map \Re z}$ $\ds$ $=$ $\ds -\map \Im w \, \map \Im z) + i \, \map \Im w \, \map \Re z$ as $\map \Re w = 0$

This equation shows that $\map \Re {w z} = -\map \Im w \, \map \Im z$, and $\map \Im {w c} = \map \Im w \, \map \Re z$.

This proves $(2)$.

$\blacksquare$


text:
## anonymous one year ago Which of the following is not considered a cause of the Enlightenment? increased availability of printed books the Scientific Revolution decline in the education system the Renaissance

1. jagr2713
2. jagr2713

You there @JamalH

3. anonymous

ye

4. anonymous

im gonna say D or B?

5. jagr2713

B is incorrect b.c 'Inspiration came from the Scientific Revolution. The discovery that the earth was not at the center of the universe and the discovery that God had not created everything lead to a new way of thought where the church’s validity was questioned. Religion:"

6. anonymous

ok so ima say C then

7. anonymous

thnx again

8. jagr2713

Nope not C o_o

9. anonymous

i mean B

10. jagr2713

Not B either scientific revolution is a cause.

11. jagr2713

Do you think A is correct....?

12. anonymous

it would seem so

13. jagr2713

Well its more of an effect b.c The cause is the invention of the printing press then the effect is increased availability of printed books

14. jagr2713

So what answer choice is left?

15. anonymous

I will say D then.

16. jagr2713

Correct :D $\huge{\color{purple}{\textbf{W}} \color{orange}{\cal{E}} \color{green}{\mathbb{L}} \color{blue}{\mathsf{C}} \color{maroon}{\rm{O}} \color{red}{\tt{M}} \color{gold}{\tt{E}} \space \color{orchid}{\mathbf{T}} \color{Navy}{\mathsf{O}} \space \color{OrangeRed}{\boldsymbol{O}} \color{Olive}{\mathbf{P}} \color{Lime}{\textbf{E}} \color{DarkOrchid}{\mathsf{N}} \color{Tan}{\mathtt{S}} \color{magenta}{\mathbb{T}} \color{goldenrod}{\mathsf{U}} \color{ForestGreen}{\textbf{D}} \color{Salmon}{\mathsf{Y}} \ddot \smile }$ if you want to know more about this site, Here is a tutorial about this site : http://openstudy.com/study#/updates/5525c0fce4b030ceb3f357e8

17. anonymous

awsome thnx

18. jagr2713

Anytime :D


text:
## Cryptology ePrint Archive: Report 2010/199

A Framework for Fully-Simulatable $t$-out-of-$n$ Oblivious Transfer

Bing Zeng and Christophe Tartary and Chingfang Hsu and Xueming Tang

Abstract: Oblivious transfer is a fundamental building block for multiparty computation protocols. In this paper, we present a generally realizable framework for fully-simulatable $t$-out-of-$n$ oblivious transfer ($\mbox{OT}^{n}_{t}$) with security against non-adaptive malicious adversaries in the plain mode. Our construction relies on a single cryptographic primitive which is a variant of smooth projective hashing (SPH). A direct consequence of our work is that the existence of protocols for $\mbox{OT}^{n}_{t}$ is reduced to the existence of this SPH variant. Before this paper, the only known reductions provided half-simulatable security and every known efficient protocol involved at least two distinct cryptographic primitives. We show how to instantiate this new SPH variant under not only the decisional Diffie-Hellman assumption, the decisional $N$-th residuosity assumption and the decisional quadratic residuosity assumption as currently existing SPH constructions, but also the learning with errors problem. Our framework only needs $4$ communication rounds, which implies that it is more round-efficient than known protocols holding identical features.

Category / Keywords: cryptographic protocols / oblivious transfer,public-key cryptography, quantum cryptography,lattice techniques

Date: received 9 Apr 2010, last revised 13 Jan 2015

Contact author: zeng bing zb at gmail com

Available format(s): PDF | BibTeX Citation

Note: Submitted for Publication.

Short URL: ia.cr/2010/199

[ Cryptology ePrint archive ]


text:
# Math Help - Subspace: why?

1. ## Subspace: why?

I'm sure you seen this theorem in one wording or the other that W is a subspace of V iff: 1) W is nonempty, 2) W is closed under multiplication by scalars, and 3) W is closed under vector addition.

One of the questions in the textbook asks "Explain why a subset of a vector space must be nonempty in order for it to be a subspace."

I was guessing that if W was empty, then #2 and 3 in that theorem would be disrupted since there's nothing to multiply the scalars with in #2.

What's your take on this question?

2. Originally Posted by seadog
I'm sure you seen this theorem in one wording or the other that W is a subspace of V iff: 1) W is nonempty, 2) W is closed under multiplication by scalars, and 3) W is closed under vector addition.

One of the questions in the textbook asks "Explain why a subset of a vector space must be nonempty in order for it to be a subspace."

I was guessing that if W was empty, then #2 and 3 in that theorem would be disrupted since there's nothing to multiply the scalars with in #2.

What's your take on this question?
Strictly speaking, if W has no members, the requirements regarding addition of vectors and scalar product are "vacuously" true: they are of the form "if A then B" and "A" is true. Such a statement is true whether or not B is.

You must show that a set satisfying #2 and #3 does not satisfy at least one of the requirements for a subspace. The standard definition of "subspace" of a vector space is that it is a subset of the vector space that forms a vector space itself with the addition and scalar multiplication "inherited" from the vecto space. And one of the requirements for a vector space is that it have a "0" vector.


text:
# Author

Sort by: Order: Results:

• (Elsevier, 2016-11)
We consider the possibility of grand unification of the SU(3)c⊗SU(3)L⊗U(1)X model in an SU(6) gauge unification group. Two possibilities arise. Unlike other conventional grand unified theories, in SU(6) one can embed the ...
• (Cornell University Library, 2016-08)
We consider the possibility of grand unification of the SU(3)c⊗SU(3)L⊗U(1)X model in an SU(6) gauge unification group. Two possibilities arise. Unlike other conventional grand unified theories, in SU(6) one can embed the ...
• (Springer Berlin Heidelberg, 2016-01)
Recent experimental results from the LHCb, BaBar and Belle collaborations on the semitauonic decays of B meson, B¯¯¯¯→D(∗)τν¯¯¯, showing a significant deviation from the Standard Model (SM), hint towards a new physics ...
• (Cornell University Library, 2015-11)
Recent experimental results from the LHCb, BaBar and Belle collaborations on the semitauonic decays of B meson, \bar{B}\rightarrow D^{(\ast)}\tau \bar{\nu}, showing a significant deviation from the Standard Model (SM), ...
• (IOP Publishing, 2015-09)
We review the non-supersymmetric (Extended) Left-Right Symmetric Models (LRSM) and low energy E6-based models to investigate if they can explain both the recently detected excess eejj signal at CMS and leptogenesis. The ...
• (Cornell University Library, 2015-01)
We show that superstring inspired E6 models can explain both the recently detected excess eejj and $e \slashed p_T jj$ signals at CMS, and also allow for leptogenesis. Working in a R-parity conserving low energy supersymmetric ...
• (American Physical Society, 2015-03)
We show that superstring-inspired E6 models can explain both the recently detected excess eejj and epTjj signals at CMS and also allow for leptogenesis. Working in an R-parity conserving, low-energy supersymmetric effective ...
• (Cornell University Library, 2015-07)
We study the superstring inspired E6 model motivated U(1)N extension of the supersymmetric standard model to explore the possibility of explaining the recent excess CMS events and the baryon asymmetry of the universe in ...
• (American Physical Society, 2016-01)
We study the superstring inspired E6 model motivated U(1)N extension of the supersymmetric standard model to explore the possibility of explaining the recent excess CMS events and the baryon asymmetry of the Universe in ...
• (American Physical Society, 2016-04)
we propose a possible explanation for the recent diphoton excess reported by ATLAS and CMS Collaborations at around a 750 GeV diphoton invariant mass within the framework of the E 6 -motivated alternative left-right ...
• (American Physical Society, 2015)
We point out that the discovery of a right-handed charged gauge boson W±R with mass of around a few TeV, for example through a signal of two leptons and two jets that has been reported by CMS to have a 2.8σ local excess ...
• (Cornell University Library, 2015-03)
We study the left-right symmetric extensions of the Standard Model (LRSM) and point out that the discovery of a right-handed charged gauge boson W±R with mass in the TeV range will have profound consequences for leptogenesis. ...
• (Cornell University Library, 2016-01)
The recent diphoton excess signal at an invariant mass of 750 GeV can be interpreted in the framework of left-right symmetric models with additional scalar singlets and vector-like fermions. We propose a minimal scenario ...
• (Elsevier, 2016-06)
The recent diphoton excess signal at an invariant mass of 750 GeV can be interpreted in the framework of left-right symmetric models with additional scalar singlets and vector-like fermions. We propose a minimal scenario ...
• (Cornell University Library, 2016-05)
We present a minimal framework of U(1)B−L gauge extension of the Standard Model explaining dark matter abundance and matter-antimatter asymmetry simultaneously through an attractive mechanism of TeV scale WIMPy leptogenesis, ...
• (Elsevier, 2016-05)
We study a cogenesis mechanism in which the observed baryon asymmetry of the universe and the dark matter abundance can be produced simultaneously at low reheating temperature without violating baryon number in the fundamental ...
• (Cornell University Library, 2015-11)
We propose a realization of mass varying neutrino dark energy in two extensions of the Standard Model (SM) with a dynamical neutrino mass related to the acceleron field while satisfying the naturalness. In the first scenario ...
• (Springer Berlin Heidelberg, 2016-05)
We propose a realization of mass varying neutrino dark energy in two extensions of the Standard Model (SM) with a dynamical neutrino mass related to the acceleron field while satisfying the naturalness. In the first scenario ...
• (American Physical Society, 2018-02)
We discuss a class of left-right symmetric theories with a universal seesaw mechanism for fermion masses and mixing and the implications for neutrinoless double beta (0νββ)decay where neutrino masses are governed by natural ...
• (Cornell University Library, 2016-01)
We discuss a class of left-right symmetric theories with a universal seesaw mechanism for fermion masses and mixing and the implications for neutrinoless double beta (0νββ) decay where neutrino masses are governed by natural ...