任务指令: 你需要根据以下这个金融逻辑, 组合创新 alpha
**Name**
Brand Sentiment Lag Premium Factor
**Assumption**
Consumer sentiment toward a brand (e.g., social media praise, search volume, user ratings) typically accumulates gradually after marketing campaigns or product launches, but the market’s pricing of brand value often lags behind sentiment shifts. When brand sentiment rises persistently but stock prices have not yet fully reflected it, a “sentiment-price” mispricing opportunity emerges; conversely, when sentiment turns downward while prices remain elevated, it may signal an impending correction. This factor captures the time-lag effect between brand sentiment and price reaction, building an alpha logic based on “sentiment momentum leading price momentum.”
**Implementation**
Construct a “Brand Sentiment Composite Index” by integrating multi-source data (e.g., social media sentiment scores, brand search trends, user rating trajectories, e-commerce review sentiment). Apply a time-series smoothing operator (e.g., ts_ewma) to filter out short-term noise. Use the ts_lag operator to shift the sentiment index by 3–6 months, then compute rolling correlations with concurrent stock returns. Establish long positions in companies where sentiment leads price momentum with statistically significant positive correlation; establish short positions in companies where sentiment has peaked but prices continue rising. Apply industry-neutralization to mitigate industry-specific sentiment cycles.
**Alpha Factor Optimization Suggestions**
It is recommended to introduce a “sentiment inflection point detection operator” using ts_slope or ts_change_rate to identify trend reversals, triggering position adjustments only after confirmation to reduce false signals. Additionally, overlay “brand moat strength” as a moderating variable — in industries with high brand loyalty and low substitutability, the sentiment lag effect is more pronounced, allowing higher weights for such companies. Furthermore, consider dynamically rebalancing the sentiment factor around quarterly earnings releases to capture accelerated pricing effects from earnings realization.

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输出格式：
输出必须是且仅是纯文本。
每一行是一个完整、独立、语法正确的WebSim表达式。
严禁任何形式的解释、编号、标点包裹（如引号）、Markdown格式或额外文本。
===================== !!! 重点(输出方式) !!! =====================
现在，请严格遵守以上所有规则，开始生成可立即在WebSim中运行的复合因子表达式。
不要自行假设, 你需要用到的操作符 和 数据集, 必须从我提供给你的里面查找, 并严格按照里面的使用方法进行组合
**输出格式**(一行一个表达式, 每个表达式中间需要添加一个空行, 只要表达式本身, 不需要赋值, 不要解释, 不需要序号, 也不要输出多余的东西)：
表达式
表达式
表达式
...
表达式
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重申：请确保所有表达式都使用WorldQuant WebSim平台函数，不要使用pandas、numpy或其他Python库函数。输出必须是一行有效的WQ表达式。
以下是我的账号有权限使用的操作符, 请严格按照操作符, 以及我提供的数据集, 进行生成,组合 20 个alpha：
不要自行假设, 你需要用到的操作符 和 数据集, 必须从我提供给你的里面查找, 并严格按照里面的使用方法进行组合

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注意!!以下操作符不能使用事件类的数据集, 请勿类似的操作：
Operator ts_product does not support event inputs
Operator ts_zscore does not support event inputs
Operator ts_mean does not support event inputs
Operator ts_scale does not support event inputs
Operator add does not support event inputs
Operator sign does not support event inputs
Operator subtract does not support event inputs
Operator ts_delta does not support event inputs
Operator ts_rank does not support event inputs
Operator greater does not support event inputs
Operator ts_av_diff does not support event inputs
Operator ts_quantile does not support event inputs
Operator ts_count_nans does not support event inputs
Operator ts_covariance does not support event inputs
Operator ts_arg_min does not support event inputs
Operator divide does not support event inputs
Operator ts_corr does not support event inputs
Operator multiply does not support event inputs
Operator if_else does not support event inputs
Operator ts_sum does not support event inputs
Operator ts_delay does not support event inputs
Operator group_zscore does not support event inputs
Operator ts_arg_max does not support event inputs
Operator ts_std_dev does not support event inputs
Operator ts_backfill does not support event inputs

以下是我的账号有权限使用的操作符, 请严格按照操作符, 进行生成,组合因子

========================= 操作符开始 =======================================
注意: Operator: 后面的是操作符(是可以使用的),
Description: 此字段后面的是操作符对应的描述或使用说明(禁止使用, 仅供参考), Description字段后面的内容是使用说明, 不是操作符
特别注意!!!! 必须按照操作符字段Operator的使用说明生成 alphaOperator: abs(x)
Description: Absolute value of x
Operator: add(x, y, filter = false)
Description: Add all inputs (at least 2 inputs required). If filter = true, filter all input NaN to 0 before adding
Operator: densify(x)
Description: Converts a grouping field of many buckets into lesser number of only available buckets so as to make working with grouping fields computationally efficient
Operator: divide(x, y)
Description: x / y
Operator: inverse(x)
Description: 1 / x
Operator: log(x)
Description: Natural logarithm. For example: Log(high/low) uses natural logarithm of high/low ratio as stock weights.
Operator: max(x, y, ..)
Description: Maximum value of all inputs. At least 2 inputs are required
Operator: min(x, y ..)
Description: Minimum value of all inputs. At least 2 inputs are required
Operator: multiply(x ,y, ... , filter=false)
Description: Multiply all inputs. At least 2 inputs are required. Filter sets the NaN values to 1
Operator: power(x, y)
Description: x ^ y
Operator: reverse(x)
Description: - x
Operator: sign(x)
Description: if input > 0, return 1; if input < 0, return -1; if input = 0, return 0; if input = NaN, return NaN;
Operator: signed_power(x, y)
Description: x raised to the power of y such that final result preserves sign of x
Operator: sqrt(x)
Description: Square root of x
Operator: subtract(x, y, filter=false)
Description: x-y. If filter = true, filter all input NaN to 0 before subtracting
Operator: and(input1, input2)
Description: Logical AND operator, returns true if both operands are true and returns false otherwise
Operator: if_else(input1, input2, input 3)
Description: If input1 is true then return input2 else return input3.
Operator: input1 < input2
Description: If input1 < input2 return true, else return false
Operator: input1 <= input2
Description: Returns true if input1 <= input2, return false otherwise
Operator: input1 == input2
Description: Returns true if both inputs are same and returns false otherwise
Operator: input1 > input2
Description: Logic comparison operators to compares two inputs
Operator: input1 >= input2
Description: Returns true if input1 >= input2, return false otherwise
Operator: input1!= input2
Description: Returns true if both inputs are NOT the same and returns false otherwise
Operator: is_nan(input)
Description: If (input == NaN) return 1 else return 0
Operator: not(x)
Description: Returns the logical negation of x. If x is true (1), it returns false (0), and if input is false (0), it returns true (1).
Operator: or(input1, input2)
Description: Logical OR operator returns true if either or both inputs are true and returns false otherwise
Operator: days_from_last_change(x)
Description: Amount of days since last change of x
Operator: hump(x, hump = 0.01)
Description: Limits amount and magnitude of changes in input (thus reducing turnover)
Operator: kth_element(x, d, k)
Description: Returns K-th value of input by looking through lookback days. This operator can be used to backfill missing data if k=1
Operator: last_diff_value(x, d)
Description: Returns last x value not equal to current x value from last d days
Operator: ts_arg_max(x, d)
Description: Returns the relative index of the max value in the time series for the past d days. If the current day has the max value for the past d days, it returns 0. If previous day has the max value for the past d days, it returns 1
Operator: ts_arg_min(x, d)
Description: Returns the relative index of the min value in the time series for the past d days; If the current day has the min value for the past d days, it returns 0; If previous day has the min value for the past d days, it returns 1.
Operator: ts_av_diff(x, d)
Description: Returns x - tsmean(x, d), but deals with NaNs carefully. That is NaNs are ignored during mean computation
Operator: ts_backfill(x,lookback = d, k=1, ignore="NAN")
Description: Backfill is the process of replacing the NAN or 0 values by a meaningful value (i.e., a first non-NaN value)
Operator: ts_corr(x, y, d)
Description: Returns correlation of x and y for the past d days
Operator: ts_count_nans(x ,d)
Description: Returns the number of NaN values in x for the past d days
Operator: ts_covariance(y, x, d)
Description: Returns covariance of y and x for the past d days
Operator: ts_decay_linear(x, d, dense = false)
Description: Returns the linear decay on x for the past d days. Dense parameter=false means operator works in sparse mode and we treat NaN as 0. In dense mode we do not.
Operator: ts_delay(x, d)
Description: Returns x value d days ago
Operator: ts_delta(x, d)
Description: Returns x - ts_delay(x, d)
Operator: ts_mean(x, d)
Description: Returns average value of x for the past d days.
Operator: ts_product(x, d)
Description: Returns product of x for the past d days
Operator: ts_quantile(x,d, driver="gaussian" )
Description: It calculates ts_rank and apply to its value an inverse cumulative density function from driver distribution. Possible values of driver (optional ) are "gaussian", "uniform", "cauchy" distribution where "gaussian" is the default.
Operator: ts_rank(x, d, constant = 0)
Description: Rank the values of x for each instrument over the past d days, then return the rank of the current value + constant. If not specified, by default, constant = 0.
Operator: ts_regression(y, x, d, lag = 0, rettype = 0)
Description: Returns various parameters related to regression function
Operator: ts_scale(x, d, constant = 0)
Description: Returns (x - ts_min(x, d)) / (ts_max(x, d) - ts_min(x, d)) + constant. This operator is similar to scale down operator but acts in time series space
Operator: ts_std_dev(x, d)
Description: Returns standard deviation of x for the past d days
Operator: ts_step(1)
Description: Returns days' counter
Operator: ts_sum(x, d)
Description: Sum values of x for the past d days.
Operator: ts_zscore(x, d)
Description: Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean: (x - tsmean(x,d)) / tsstddev(x,d). This operator may help reduce outliers and drawdown.
Operator: normalize(x, useStd = false, limit = 0.0)
Description: Calculates the mean value of all valid alpha values for a certain date, then subtracts that mean from each element
Operator: quantile(x, driver = gaussian, sigma = 1.0)
Description: Rank the raw vector, shift the ranked Alpha vector, apply distribution (gaussian, cauchy, uniform). If driver is uniform, it simply subtract each Alpha value with the mean of all Alpha values in the Alpha vector
Operator: rank(x, rate=2)
Description: Ranks the input among all the instruments and returns an equally distributed number between 0.0 and 1.0. For precise sort, use the rate as 0
Operator: scale(x, scale=1, longscale=1, shortscale=1)
Description: Scales input to booksize. We can also scale the long positions and short positions to separate scales by mentioning additional parameters to the operator
Operator: winsorize(x, std=4)
Description: Winsorizes x to make sure that all values in x are between the lower and upper limits, which are specified as multiple of std.
Operator: zscore(x)
Description: Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean
Operator: vec_avg(x)
Description: Taking mean of the vector field x
Operator: vec_sum(x)
Description: Sum of vector field x
Operator: bucket(rank(x), range="0, 1, 0.1" or buckets = "2,5,6,7,10")
Description: Convert float values into indexes for user-specified buckets. Bucket is useful for creating group values, which can be passed to GROUP as input
Operator: trade_when(x, y, z)
Description: Used in order to change Alpha values only under a specified condition and to hold Alpha values in other cases. It also allows to close Alpha positions (assign NaN values) under a specified condition
Operator: group_backfill(x, group, d, std = 4.0)
Description: If a certain value for a certain date and instrument is NaN, from the set of same group instruments, calculate winsorized mean of all non-NaN values over last d days
Operator: group_mean(x, weight, group)
Description: All elements in group equals to the mean
Operator: group_neutralize(x, group)
Description: Neutralizes Alpha against groups. These groups can be subindustry, industry, sector, country or a constant
Operator: group_rank(x, group)
Description: Each elements in a group is assigned the corresponding rank in this group
Operator: group_scale(x, group)
Description: Normalizes the values in a group to be between 0 and 1. (x - groupmin) / (groupmax - groupmin)
Operator: group_zscore(x, group)
Description: Calculates group Z-score - numerical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. zscore = (data - mean) / stddev of x for each instrument within its group.
========================= 操作符结束 =======================================

========================= 数据字段开始 =======================================
注意: data_set_name: 后面的是数据字段(可以使用), description: 此字段后面的是数据字段对应的描述或使用说明(不能使用), description_cn字段后面的内容是中文使用说明(不能使用)

{'data_set_name': '可以使用:forward_price_120', 'description': '不可使用,仅供参考:Forward price at 120 days derived from a synthetic long option with payoff similar to long stock + option dynamics. Combination of long ATM call and short ATM put.'}
{'data_set_name': '可以使用:fnd6_ciother', 'description': '不可使用,仅供参考:Comp. Inc. - Other Adj.'}
{'data_set_name': '可以使用:fnd6_eventv110_gdwlieps12', 'description': '不可使用,仅供参考:Impairment of Goodwill Basic EPS Effect 12MM'}
{'data_set_name': '可以使用:fnd6_eventv110_gdwliepsq', 'description': '不可使用,仅供参考:Impairment of Goodwill Basic EPS Effect'}
{'data_set_name': '可以使用:fnd6_newa2v1300_oiadp', 'description': '不可使用,仅供参考:Operating Income After Depreciation'}
{'data_set_name': '可以使用:fnd6_newqeventv110_gdwliaq', 'description': '不可使用,仅供参考:Impairment of Goodwill After-tax'}
{'data_set_name': '可以使用:fnd6_newqeventv110_glceaq', 'description': '不可使用,仅供参考:Gain/Loss on Sale (Core Earnings Adjusted) After-tax'}
{'data_set_name': '可以使用:fnd6_newqeventv110_spcedq', 'description': '不可使用,仅供参考:S&P Core Earnings EPS Diluted'}
{'data_set_name': '可以使用:fnd6_newqeventv110_spceeps12', 'description': '不可使用,仅供参考:S&P Core Earnings EPS Basic 12MM'}
{'data_set_name': '可以使用:fnd6_newqeventv110_spceepsq', 'description': '不可使用,仅供参考:S&P Core Earnings EPS Basic'}
{'data_set_name': '可以使用:fnd6_newqeventv110_spcep12', 'description': '不可使用,仅供参考:S&P Core Earnings 12MM - Preliminary'}
{'data_set_name': '可以使用:fnd6_newqeventv110_spcepd12', 'description': '不可使用,仅供参考:S&P Core Earnings 12MM EPS Diluted - Preliminary'}
{'data_set_name': '可以使用:fnd6_newqv1300_ciotherq', 'description': '不可使用,仅供参考:Comp Inc - Other Adj'}
{'data_set_name': '可以使用:fnd6_newqv1300_spcedq', 'description': '不可使用,仅供参考:S&P Core Earnings EPS Diluted'}
{'data_set_name': '可以使用:fnd6_newqv1300_spceepsq', 'description': '不可使用,仅供参考:S&P Core Earnings EPS Basic'}
{'data_set_name': '可以使用:fnd6_oiadps', 'description': '不可使用,仅供参考:Operating Income after Depreciation'}
{'data_set_name': '可以使用:fnd6_spce', 'description': '不可使用,仅供参考:S&P Core Earnings'}
{'data_set_name': '可以使用:anl4_netdebt_flag', 'description': '不可使用,仅供参考:Net debt - forecast type (revision/new/...)'}
{'data_set_name': '可以使用:news_max_up_amt', 'description': '不可使用,仅供参考:The after the news high minus the price at the time of the news'}
{'data_set_name': '可以使用:nws18_sse', 'description': '不可使用,仅供参考:Sentiment of phrases impacting the company'}
{'data_set_name': '可以使用:fn_comp_not_rec_stock_options_a', 'description': '不可使用,仅供参考:Unrecognized cost of unvested stock option awards.'}
{'data_set_name': '可以使用:fn_comp_not_rec_stock_options_q', 'description': '不可使用,仅供参考:Unrecognized cost of unvested stock option awards.'}
{'data_set_name': '可以使用:fn_def_tax_assets_liab_net_q', 'description': '不可使用,仅供参考:Amount, after allocation of valuation allowances and deferred tax liability, of deferred tax asset attributable to deductible differences and carryforwards, without jurisdictional netting.'}
{'data_set_name': '可以使用:fn_def_tax_liab_a', 'description': '不可使用,仅供参考:Amount, after deferred tax asset, of deferred tax liability attributable to taxable differences without jurisdictional netting.'}
{'data_set_name': '可以使用:fn_op_lease_min_pay_due_in_2y_a', 'description': '不可使用,仅供参考:Amount of required minimum rental payments for operating leases having an initial or remaining non-cancelable lease term in excess of 1 year due in the 2nd fiscal year following the latest fiscal year. Excludes interim and annual periods when interim periods are reported on a rolling approach, from latest balance sheet date.'}
========================= 数据字段结束 =======================================

以上数据字段和操作符, 按照Description说明组合, 但是每一个 alpha 组合的使用的数据字段和操作符不要过于集中, 在符合语法的情况下, 多尝试不同的组合