enterprise search – What is the KQL syntax to filter by owstaxId managed properties in SharePoint 2010?

My understanding of how to use KQL to query against the automatically created managed properties which have the form of owstaxIdProperty, that is that to query for all items with a given term, the syntax is, based on this post by Mikael Svenson:

owstaxIdProperty:"GP0|#c8a43f13-5ea1-45f2-b46d-3a1986a1cbd7"

However, when I try to enter a similar query through the query to the results.aspx page by entering a url similar to (with the # encoded as %23):

/Search/Pages/results.aspx?k=owsTaxIdProperty:"GP0|%23c8a43f13-5ea1-45f2-b46d-3a1986a1cbd7"

I obtain no results and a message as in the image below, which suggests to me that the query is getting through

enter image description here

If I write the query just as Property:TermLabel, the query works and the expected results are returned but I think this could be inaccurate if you have duplicated term labels, as I do

This question is similar but I suspect that the poster is using SharePoint 2013, rather than 2010

Another possibility is that I should be using the WssId instead of the termGuid, as is suggested in an MSDN post on “Querying on Managed Metadata Field Values in SharePoint Server 2010 (ECM)” (sorry, I can’t post more than two links)

Has anyone had success with similar queries using SharePoint 2010?

optimization – What properties of a discrete function make it a theoretically useful objective function?

A few things to get out of the way first: I’m not asking what properties the function must have such that a global optimum exists, we assume that the objective function has a (possibly non-unique) global optimum which could be theoretically found by an exhaustive search of the candidate space. I’m also using “theoretically useful” in a slightly misleading way because I really couldn’t understand how to phrase this question otherwise. A “theoretically useful cost function” the way I’m defining it is:

A function to which some theoretical optimisation algorithm can be applied such that the algorithm has a non-negligible chance of finding the global optimum in less time than exhaustive search

A few simplified, 1-dimensional examples of where this thought process came from:
graph of a bimodal function exhibiting both a global and local maxima

Here’s a function which, while not being convex or differentiable (as it’s discrete), is easily optimisable (in terms of finding the global maximum) with an algorithm such as Simulated Annealing.

graph of a boolean function with 100 0 values and a single 1 value

Here is a function which clearly cannot be a useful cost function, as this would imply that the arbitrary search problem can be classically solved faster than exhaustive search.

graph of a function which takes random discrete values

Here is a function which I do not believe can be a useful cost function, as moving between points gives no meaningful information about the direction which must be moved in to find the global maximum.

The crux of my thinking so far is along the lines of “applying the cost function to points in the neighbourhood of a point must yield some information about the location of the global optimum”. I attempted to formalise (in a perhaps convoluted manner) this as:

Consider the set $D$ representing the search space of the problem and thus the domain of the function and the undirected graph $G$, where each element of $D$ is assigned a node in $G$, and each node in $G$ has edges which connect it to its neighbours in $D$. We then remove elements from $D$ until the objective function has no non-global local optima over this domain and no plateaus exist (i.e. the value of the cost function at each point in the domain is different from the value of the cost function at each of its neighbours). Every time we remove an element $e$ from $D$, we remove the corresponding node from the graph $G$ and add edges which directly connect each neighbour of $e$ to each other, thus they become each others’ new neighbours. The number of elements which remain in the domain after this process is applied is designated $N$. If $N$ is a non-negligible proportion of $#(D)$ (i.e. significantly greater than the proportion of $#({$possible global optima$})$ to $#(D)$) then the function is a useful objective function.

Whilst this works well for the function which definitely is useful and the definitely not useful boolean function, this process applied to the random function seems incorrect, as the number of elements that would lead to a function with no local optima IS a non-negligible proportion of the total domain.

Is my definition on the right track? Is this a well known question I just can’t figure out how to find the answer to? Does there exist some optimisation algorithm that would theoretically be able to find the optimum of a completely random function faster than exhaustive search, or is my assertion that it wouldn’t be able to correct?

In conclusion, what is different about the first function that makes it a good candidate for optimisation to any other functions which are not.

Define quaternions by properties instead of coordinates

I’d like to manipulate an expression of quaternions and only use the following properties

q1+q2=q2+q1
q1**(q2+q3)=q1**q2+q1**q3
q1**(q2**q3)=(q1**q2)**q3
Conjugate(q1**q2)=Conjugate(q2)**Conjugate(q1)
q**x=x**q if x is Real
q**Conjugate(q) is always Real
Conjugate(x)=x if x is Real

closure properties – How to show that language L is NOT context-free?

True or false: To show that a language L is not context-free, one can alternatively show that the union between L and a known context-free language is not context-free.

I know that you can prove closure under context-free languages using union, but does the above work, too? Any help you can provide would be greatly appreciated!

nt.number theory – Full measure properties for Zariski open subsets in $p$-adic situation

Let $F$ be a $p$-adic field and let $X$ be a smooth integral variety over $F$ (I am chiefly interested in the case when $X$ is a connected reductive group over $F$). Let $U$ be a non-empty open subset of $X$ with complement $Z$.

We can endow $X(F)$ with the Serre-Oesterle measure (e.g. as in (1,Section 2.2) or (2, Section 7.4))–this is just the standard measure coming from a top form of $X$).

My question is then whether one knows a simple proof/reference for the following:

The subset $Z(F)$ of $X(F)$ has measure zero.

I think this is proven in (1, Lemma 2.14)–but this is concerned with a more specific context which makes it non-ideal as a reference.

Any help is appreciated!

(1) http://www.math.uni-bonn.de/people/huybrech/Magni.pdf

(2) Igusa, J.I., 2007. An introduction to the theory of local zeta functions (Vol. 14). American Mathematical Soc..

firebase – Show data from firestore two properties

I want to show data which meets the following 2 conditions:

  • The ‘done’ property is false, and
  • If ‘done’ is true, then only show today’s done items (serverTimeStamp)

How could I go about achieving this:

Currently I have the following which only returns items where ‘done’ is false.

yield* userDoc.todoCollection
        .orderBy('serverTimeStamp', descending: true)
        .snapshots()
        .map(
          (snapshot) => snapshot.documents
              .map((doc) => TodoDto.fromFirestore(doc).toDomain()),
        )
        .map(
          (todos) => right<TodoFailure, KtList<TodoItem>>(
            todos
                .where(
                  (todo) =>
                      !todo.done,
                )
                .toImmutableList(),
          ),
        )

calculus and analysis – Simplifying expressions using elementary properties of integrals

I want to be able to use Simplify (or FullSimplify) to simplify expressions involving, for example, sums of integrals, for instance turning

$$ int_a^b f(x),dx + int_b^c f(x),dx $$

into

$$ int_a^c f(x),dx $$

Certainly this can be done with replacement rules, but doing so requires cobbling together a lot of special cases like this one:

HoldPattern(Integrate(u_, {x_, a_, b_}) + Integrate(u_, {x_, b_, c_}) + rest___) :>
  Integrate(u, {x, a, c})

Using rules like than requires fiddly mixing of steps with Expand, Simplify, ReplaceAll, ReplaceRepeated, and on and on, and the whole process is annoying and error prone, especially if you screw up your rules. On top of that, you have to worry about ordering them properly in order to get them to fire in ways that lead to simplification.

All in all, the process is a real pain in the neck.

I keep wanting to find a better way. Is there one?

On Reflection Properties of Convex Regions

It is well known that any ray of light passing thru a focus of an ellipse will pass thru the other focus after a single reflection from the ellipse boundary. If A and B are the foci of an ellipse, this property of rays holds both ways (those passing thru A meet at B and vice versa).

  1. Is there a closed convex region C with the property: there exists a pair of points A and B within C such that all rays thru A will reflect once on C and pass thru B but not all rays thru B will pass thru A after one reflection from C?

  2. Is there a closed convex region C such that: there is a pair of points A and B in the interior such that all rays thru A pass thru B after exactly 2 reflections from C?
    Note: This question can have ‘one-way’ (convergence only of rays thru A at B) and ‘both-ways’ variants.

non archimedean fields – Model-theoretic properties of slice theories

$newcommand{DOAG}{mathsf{DOAG}}newcommand{slice}{{downarrow}}$I am still a newcomer to model theory, but I am interested in some applications to non-archimedean geometry. I wondered about the following:

Let $G$ be a fixed totally ordered, divisible abelian group. Let $GsliceDOAG$ denote the theory of totally ordered divisible abelian groups over $G$. By this I mean the theory having:

  1. One sort of group elements.

    • A constant symbol $0$, a function symbols $+$, a relation symbol $<$.
    • For each element $g in G$ a constant symbol, also denoted by $g$.
    • Axioms describing that models of $GsliceDOAG$ are totally ordered abelian groups.
    • Axioms describing that the constant symbols $g$ behave like the corresponding elements of $G$ with respect to the group structure symbols and the order symbol.

In other words, models $H$ of $GsliceDOAG$ should be totally ordered, divisible abelian groups equipped with an embedding of DOAGs $G to H$.

Now it is well-known that the ordinary theory $DOAG$ of totoally ordered, divisible abelian groups satisfies quantifier elimination, elimination of imaginaries, completeness, model-completeness,… (I am mainly interested in the first and second property).

Are these properties inherited by $Gslice DOAG$?

I have analogous questions regarding algebraically closed fields, and the one- and two-sorted theories of algebraically closed valued fields. Therefore, my other question is:

Are such “slice theories” (borrowing terminology from category theory) considered in model theory and does my first question have an answer in this generality?

gtk3 – Where can I find better documentation for the CSS properties of GTK widgets?

I’m working on learning the CSS styling part of GTK3, and I have noticed that the reference GTK documention talks about the CSS nodes that get created, but not what properties are valid for the component.

For instance, GtkSeparator includes this as the full CSS documentation:

GtkSeparator has a single CSS node with name separator. The node gets one of the .horizontal or .vertical style classes.

This describes to me how to address this component in the stylesheet, but it took an hour of trial and error to figure out that the color for this component is controlled by the background-color attribute, not the color attribute.

I am having similar problems with GtkComboBox where the documentation lists the node hierarchy, but not what the nodes correspond to visually or what properties are valid for them.

Is there more detailed documentation for each component, especially listing valid properties and what the properties correspond to visually?